Require Import ssreflect ssrfun ssrbool.
Require Import Generic.lemmas Generic.wlog Generic.modulo120.
Require Import PG32.pg32_inductive PG32.pg32_spreads_packings PG32.pg32_spreads_collineations.
Require Import List.
Require Import FunInd.
Require Import Lia.

(* ~~~~~~~~~~ CLASS 0 ~~~~~~~~~~ *)
(* P0 : S0 S9 S19 S24 S36 S46 S53 ->
   P3 : S0 S9 S20 S28 S35 S40 S55  *)
Definition fp0_3 (p:Point) := match p with P0 => P10 | P1 => P3 | P2 => P14 | P3 => P1 | P4 => P8 | P5 => P5 | P6 => P12 | P7 => P13 | P8 => P4 | P9 => P9 | P10 => P0 | P11 => P11 | P12 => P6 | P13 => P7 | P14 => P2 end.
Definition fl0_3 (l:Line) := match l with L0 => L19 | L1 => L8 | L2 => L30 | L3 => L25 | L4 => L4 | L5 => L34 | L6 => L13 | L7 => L20 | L8 => L1 | L9 => L15 | L10 => L21 | L11 => L22 | L12 => L12 | L13 => L6 | L14 => L14 | L15 => L9 | L16 => L31 | L17 => L27 | L18 => L23 | L19 => L0 | L20 => L7 | L21 => L10 | L22 => L11 | L23 => L18 | L24 => L24 | L25 => L3 | L26 => L32 | L27 => L17 | L28 => L28 | L29 => L29 | L30 => L2 | L31 => L16 | L32 => L26 | L33 => L33 | L34 => L5 end.

(* P3 : S0 S9 S20 S28 S35 S40 S55 ->
   P5 : S0 S9 S22 S27 S38 S44 S49  *)
Definition fp3_5 (p:Point) := match p with P0 => P8 | P1 => P4 | P2 => P11 | P3 => P1 | P4 => P10 | P5 => P6 | P6 => P13 | P7 => P12 | P8 => P3 | P9 => P7 | P10 => P0 | P11 => P14 | P12 => P5 | P13 => P9 | P14 => P2 end.
Definition fl3_5 (l:Line) := match l with L0 => L24 | L1 => L8 | L2 => L32 | L3 => L20 | L4 => L3 | L5 => L27 | L6 => L18 | L7 => L25 | L8 => L1 | L9 => L17 | L10 => L26 | L11 => L23 | L12 => L7 | L13 => L5 | L14 => L14 | L15 => L11 | L16 => L29 | L17 => L34 | L18 => L22 | L19 => L0 | L20 => L12 | L21 => L10 | L22 => L9 | L23 => L13 | L24 => L19 | L25 => L4 | L26 => L30 | L27 => L15 | L28 => L33 | L29 => L31 | L30 => L2 | L31 => L16 | L32 => L21 | L33 => L28 | L34 => L6 end.

(* P5 : S0 S9 S22 S27 S38 S44 S49 ->
   P6 : S0 S10 S16 S28 S33 S47 S53  *)
Definition fp5_6 (p:Point) := match p with P0 => P6 | P1 => P9 | P2 => P12 | P3 => P13 | P4 => P8 | P5 => P3 | P6 => P2 | P7 => P10 | P8 => P11 | P9 => P0 | P10 => P5 | P11 => P4 | P12 => P1 | P13 => P14 | P14 => P7 end.
Definition fl5_6 (l:Line) := match l with L0 => L33 | L1 => L32 | L2 => L15 | L3 => L34 | L4 => L2 | L5 => L7 | L6 => L31 | L7 => L18 | L8 => L29 | L9 => L10 | L10 => L4 | L11 => L23 | L12 => L21 | L13 => L30 | L14 => L26 | L15 => L16 | L16 => L9 | L17 => L20 | L18 => L5 | L19 => L28 | L20 => L11 | L21 => L6 | L22 => L25 | L23 => L3 | L24 => L24 | L25 => L27 | L26 => L8 | L27 => L22 | L28 => L19 | L29 => L1 | L30 => L12 | L31 => L13 | L32 => L14 | L33 => L0 | L34 => L17 end.

(* P6 : S0 S10 S16 S28 S33 S47 S53 ->
   P9 : S0 S10 S17 S24 S37 S44 S55  *)
Definition fp6_9 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P10 | P4 => P7 | P5 => P9 | P6 => P8 | P7 => P12 | P8 => P13 | P9 => P11 | P10 => P14 | P11 => P5 | P12 => P4 | P13 => P6 | P14 => P3 end.
Definition fl6_9 (l:Line) := match l with L0 => L0 | L1 => L13 | L2 => L18 | L3 => L16 | L4 => L14 | L5 => L17 | L6 => L15 | L7 => L3 | L8 => L6 | L9 => L1 | L10 => L5 | L11 => L2 | L12 => L4 | L13 => L9 | L14 => L12 | L15 => L8 | L16 => L7 | L17 => L10 | L18 => L11 | L19 => L19 | L20 => L25 | L21 => L34 | L22 => L30 | L23 => L22 | L24 => L28 | L25 => L31 | L26 => L26 | L27 => L21 | L28 => L33 | L29 => L29 | L30 => L23 | L31 => L20 | L32 => L32 | L33 => L24 | L34 => L27 end.

(* P9 : S0 S10 S17 S24 S37 S44 S55 ->
   P11 : S0 S10 S20 S31 S36 S43 S49  *)
Definition fp9_11 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl9_11 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P11 : S0 S10 S20 S31 S36 S43 S49 ->
   P13 : S0 S12 S17 S27 S36 S47 S48  *)
Definition fp11_13 (p:Point) := match p with P0 => P5 | P1 => P7 | P2 => P13 | P3 => P12 | P4 => P10 | P5 => P4 | P6 => P2 | P7 => P8 | P8 => P14 | P9 => P0 | P10 => P6 | P11 => P3 | P12 => P1 | P13 => P11 | P14 => P9 end.
Definition fl11_13 (l:Line) := match l with L0 => L28 | L1 => L30 | L2 => L17 | L3 => L27 | L4 => L2 | L5 => L12 | L6 => L29 | L7 => L13 | L8 => L31 | L9 => L10 | L10 => L3 | L11 => L22 | L12 => L26 | L13 => L32 | L14 => L21 | L15 => L16 | L16 => L11 | L17 => L25 | L18 => L6 | L19 => L33 | L20 => L9 | L21 => L5 | L22 => L20 | L23 => L4 | L24 => L19 | L25 => L34 | L26 => L8 | L27 => L23 | L28 => L24 | L29 => L1 | L30 => L7 | L31 => L18 | L32 => L14 | L33 => L0 | L34 => L15 end.

(* P13 : S0 S12 S17 S27 S36 S47 S48 ->
   P15 : S0 S12 S19 S31 S37 S40 S50  *)
Definition fp13_15 (p:Point) := match p with P0 => P4 | P1 => P8 | P2 => P11 | P3 => P0 | P4 => P3 | P5 => P7 | P6 => P12 | P7 => P13 | P8 => P10 | P9 => P6 | P10 => P1 | P11 => P14 | P12 => P9 | P13 => P5 | P14 => P2 end.
Definition fl13_15 (l:Line) := match l with L0 => L24 | L1 => L1 | L2 => L26 | L3 => L25 | L4 => L7 | L5 => L23 | L6 => L17 | L7 => L20 | L8 => L8 | L9 => L18 | L10 => L32 | L11 => L27 | L12 => L3 | L13 => L11 | L14 => L14 | L15 => L5 | L16 => L29 | L17 => L22 | L18 => L34 | L19 => L0 | L20 => L4 | L21 => L2 | L22 => L6 | L23 => L15 | L24 => L19 | L25 => L12 | L26 => L21 | L27 => L13 | L28 => L28 | L29 => L31 | L30 => L10 | L31 => L16 | L32 => L30 | L33 => L33 | L34 => L9 end.

(* P15 : S0 S12 S19 S31 S37 S40 S50 ->
   P16 : S0 S12 S22 S26 S33 S43 S55  *)
Definition fp15_16 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl15_16 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P16 : S0 S12 S22 S26 S33 S43 S55 ->
   P18 : S0 S13 S16 S26 S37 S46 S49  *)
Definition fp16_18 (p:Point) := match p with P0 => P13 | P1 => P5 | P2 => P7 | P3 => P2 | P4 => P12 | P5 => P4 | P6 => P10 | P7 => P8 | P8 => P6 | P9 => P14 | P10 => P0 | P11 => P9 | P12 => P3 | P13 => P11 | P14 => P1 end.
Definition fl16_18 (l:Line) := match l with L0 => L28 | L1 => L16 | L2 => L25 | L3 => L32 | L4 => L6 | L5 => L21 | L6 => L11 | L7 => L30 | L8 => L2 | L9 => L12 | L10 => L27 | L11 => L29 | L12 => L17 | L13 => L3 | L14 => L10 | L15 => L13 | L16 => L22 | L17 => L26 | L18 => L31 | L19 => L0 | L20 => L15 | L21 => L14 | L22 => L18 | L23 => L9 | L24 => L33 | L25 => L5 | L26 => L20 | L27 => L7 | L28 => L24 | L29 => L23 | L30 => L1 | L31 => L8 | L32 => L34 | L33 => L19 | L34 => L4 end.

(* P18 : S0 S13 S16 S26 S37 S46 S49 ->
   P21 : S0 S13 S19 S28 S38 S43 S48  *)
Definition fp18_21 (p:Point) := match p with P0 => P5 | P1 => P13 | P2 => P7 | P3 => P8 | P4 => P14 | P5 => P6 | P6 => P0 | P7 => P12 | P8 => P10 | P9 => P2 | P10 => P4 | P11 => P3 | P12 => P1 | P13 => P9 | P14 => P11 end.
Definition fl18_21 (l:Line) := match l with L0 => L28 | L1 => L27 | L2 => L2 | L3 => L30 | L4 => L17 | L5 => L12 | L6 => L29 | L7 => L6 | L8 => L25 | L9 => L11 | L10 => L16 | L11 => L21 | L12 => L32 | L13 => L26 | L14 => L22 | L15 => L3 | L16 => L10 | L17 => L31 | L18 => L13 | L19 => L24 | L20 => L8 | L21 => L18 | L22 => L20 | L23 => L14 | L24 => L19 | L25 => L23 | L26 => L9 | L27 => L34 | L28 => L33 | L29 => L15 | L30 => L7 | L31 => L5 | L32 => L4 | L33 => L0 | L34 => L1 end.

(* P21 : S0 S13 S19 S28 S38 S43 S48 ->
   P22 : S0 S13 S22 S24 S35 S47 S50  *)
Definition fp21_22 (p:Point) := match p with P0 => P5 | P1 => P13 | P2 => P7 | P3 => P8 | P4 => P14 | P5 => P6 | P6 => P0 | P7 => P12 | P8 => P10 | P9 => P2 | P10 => P4 | P11 => P3 | P12 => P1 | P13 => P9 | P14 => P11 end.
Definition fl21_22 (l:Line) := match l with L0 => L28 | L1 => L27 | L2 => L2 | L3 => L30 | L4 => L17 | L5 => L12 | L6 => L29 | L7 => L6 | L8 => L25 | L9 => L11 | L10 => L16 | L11 => L21 | L12 => L32 | L13 => L26 | L14 => L22 | L15 => L3 | L16 => L10 | L17 => L31 | L18 => L13 | L19 => L24 | L20 => L8 | L21 => L18 | L22 => L20 | L23 => L14 | L24 => L19 | L25 => L23 | L26 => L9 | L27 => L34 | L28 => L33 | L29 => L15 | L30 => L7 | L31 => L5 | L32 => L4 | L33 => L0 | L34 => L1 end.

(* P22 : S0 S13 S22 S24 S35 S47 S50 ->
   P25 : S0 S15 S16 S31 S35 S44 S48  *)
Definition fp22_25 (p:Point) := match p with P0 => P13 | P1 => P5 | P2 => P7 | P3 => P11 | P4 => P1 | P5 => P9 | P6 => P3 | P7 => P12 | P8 => P2 | P9 => P10 | P10 => P4 | P11 => P0 | P12 => P14 | P13 => P6 | P14 => P8 end.
Definition fl22_25 (l:Line) := match l with L0 => L28 | L1 => L11 | L2 => L21 | L3 => L16 | L4 => L25 | L5 => L6 | L6 => L32 | L7 => L12 | L8 => L17 | L9 => L27 | L10 => L30 | L11 => L2 | L12 => L29 | L13 => L26 | L14 => L3 | L15 => L22 | L16 => L31 | L17 => L10 | L18 => L13 | L19 => L24 | L20 => L14 | L21 => L34 | L22 => L5 | L23 => L8 | L24 => L0 | L25 => L7 | L26 => L9 | L27 => L18 | L28 => L33 | L29 => L4 | L30 => L23 | L31 => L20 | L32 => L15 | L33 => L19 | L34 => L1 end.

(* P25 : S0 S15 S16 S31 S35 S44 S48 ->
   P26 : S0 S15 S17 S26 S38 S40 S53  *)
Definition fp25_26 (p:Point) := match p with P0 => P8 | P1 => P4 | P2 => P11 | P3 => P9 | P4 => P2 | P5 => P14 | P6 => P5 | P7 => P10 | P8 => P1 | P9 => P13 | P10 => P6 | P11 => P0 | P12 => P7 | P13 => P3 | P14 => P12 end.
Definition fl25_26 (l:Line) := match l with L0 => L24 | L1 => L18 | L2 => L27 | L3 => L8 | L4 => L32 | L5 => L3 | L6 => L20 | L7 => L17 | L8 => L7 | L9 => L26 | L10 => L25 | L11 => L1 | L12 => L23 | L13 => L34 | L14 => L5 | L15 => L29 | L16 => L22 | L17 => L14 | L18 => L11 | L19 => L33 | L20 => L10 | L21 => L21 | L22 => L4 | L23 => L16 | L24 => L0 | L25 => L15 | L26 => L13 | L27 => L9 | L28 => L19 | L29 => L6 | L30 => L31 | L31 => L30 | L32 => L12 | L33 => L28 | L34 => L2 end.

(* P26 : S0 S15 S17 S26 S38 S40 S53 ->
   P28 : S0 S15 S20 S27 S33 S46 S50  *)
Definition fp26_28 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl26_28 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P28 : S0 S15 S20 S27 S33 S46 S50 ->
   P31 : S1 S8 S18 S31 S37 S44 S49  *)
Definition fp28_31 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P11 | P4 => P14 | P5 => P12 | P6 => P13 | P7 => P7 | P8 => P10 | P9 => P8 | P10 => P9 | P11 => P3 | P12 => P6 | P13 => P4 | P14 => P5 end.
Definition fl28_31 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L13 | L4 => L18 | L5 => L15 | L6 => L17 | L7 => L6 | L8 => L4 | L9 => L2 | L10 => L3 | L11 => L1 | L12 => L5 | L13 => L10 | L14 => L12 | L15 => L11 | L16 => L7 | L17 => L9 | L18 => L8 | L19 => L29 | L20 => L34 | L21 => L24 | L22 => L22 | L23 => L27 | L24 => L19 | L25 => L23 | L26 => L31 | L27 => L30 | L28 => L26 | L29 => L20 | L30 => L33 | L31 => L28 | L32 => L25 | L33 => L32 | L34 => L21 end.

(* P31 : S1 S8 S18 S31 S37 S44 S49 ->
   P32 : S1 S8 S19 S28 S39 S40 S53  *)
Definition fp31_32 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P14 | P4 => P11 | P5 => P12 | P6 => P13 | P7 => P9 | P8 => P8 | P9 => P7 | P10 => P10 | P11 => P4 | P12 => P5 | P13 => P6 | P14 => P3 end.
Definition fl31_32 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L18 | L4 => L13 | L5 => L17 | L6 => L15 | L7 => L11 | L8 => L8 | L9 => L12 | L10 => L10 | L11 => L7 | L12 => L9 | L13 => L4 | L14 => L1 | L15 => L6 | L16 => L2 | L17 => L5 | L18 => L3 | L19 => L19 | L20 => L27 | L21 => L31 | L22 => L23 | L23 => L22 | L24 => L24 | L25 => L34 | L26 => L29 | L27 => L20 | L28 => L33 | L29 => L26 | L30 => L30 | L31 => L21 | L32 => L32 | L33 => L28 | L34 => L25 end.

(* P32 : S1 S8 S19 S28 S39 S40 S53 ->
   P34 : S1 S8 S22 S27 S33 S47 S52  *)
Definition fp32_34 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl32_34 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P34 : S1 S8 S22 S27 S33 S47 S52 ->
   P37 : S1 S11 S17 S30 S37 S40 S52  *)
Definition fp34_37 (p:Point) := match p with P0 => P9 | P1 => P11 | P2 => P5 | P3 => P8 | P4 => P2 | P5 => P4 | P6 => P14 | P7 => P0 | P8 => P10 | P9 => P12 | P10 => P6 | P11 => P7 | P12 => P1 | P13 => P3 | P14 => P13 end.
Definition fl34_37 (l:Line) := match l with L0 => L29 | L1 => L18 | L2 => L23 | L3 => L4 | L4 => L33 | L5 => L10 | L6 => L21 | L7 => L14 | L8 => L34 | L9 => L11 | L10 => L5 | L11 => L22 | L12 => L24 | L13 => L2 | L14 => L28 | L15 => L27 | L16 => L12 | L17 => L17 | L18 => L30 | L19 => L32 | L20 => L8 | L21 => L20 | L22 => L3 | L23 => L16 | L24 => L13 | L25 => L15 | L26 => L0 | L27 => L25 | L28 => L1 | L29 => L26 | L30 => L7 | L31 => L6 | L32 => L19 | L33 => L9 | L34 => L31 end.

(* P37 : S1 S11 S17 S30 S37 S40 S52 ->
   P38 : S1 S11 S20 S28 S33 S43 S54  *)
Definition fp37_38 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl37_38 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P38 : S1 S11 S20 S28 S33 S43 S54 ->
   P40 : S1 S11 S22 S24 S39 S44 S51  *)
Definition fp38_40 (p:Point) := match p with P0 => P3 | P1 => P14 | P2 => P10 | P3 => P4 | P4 => P0 | P5 => P9 | P6 => P13 | P7 => P2 | P8 => P6 | P9 => P11 | P10 => P7 | P11 => P5 | P12 => P1 | P13 => P8 | P14 => P12 end.
Definition fl38_40 (l:Line) := match l with L0 => L19 | L1 => L1 | L2 => L21 | L3 => L15 | L4 => L22 | L5 => L12 | L6 => L20 | L7 => L6 | L8 => L31 | L9 => L9 | L10 => L14 | L11 => L27 | L12 => L23 | L13 => L13 | L14 => L30 | L15 => L25 | L16 => L8 | L17 => L4 | L18 => L34 | L19 => L26 | L20 => L7 | L21 => L24 | L22 => L17 | L23 => L5 | L24 => L2 | L25 => L3 | L26 => L0 | L27 => L33 | L28 => L18 | L29 => L29 | L30 => L10 | L31 => L16 | L32 => L32 | L33 => L11 | L34 => L28 end.

(* P40 : S1 S11 S22 S24 S39 S44 S51 ->
   P42 : S1 S13 S18 S28 S32 S47 S51  *)
Definition fp40_42 (p:Point) := match p with P0 => P14 | P1 => P10 | P2 => P3 | P3 => P8 | P4 => P5 | P5 => P1 | P6 => P12 | P7 => P9 | P8 => P4 | P9 => P0 | P10 => P13 | P11 => P2 | P12 => P11 | P13 => P7 | P14 => P6 end.
Definition fl40_42 (l:Line) := match l with L0 => L19 | L1 => L27 | L2 => L9 | L3 => L23 | L4 => L6 | L5 => L14 | L6 => L31 | L7 => L30 | L8 => L25 | L9 => L34 | L10 => L4 | L11 => L13 | L12 => L8 | L13 => L21 | L14 => L15 | L15 => L20 | L16 => L22 | L17 => L12 | L18 => L1 | L19 => L32 | L20 => L24 | L21 => L3 | L22 => L18 | L23 => L2 | L24 => L17 | L25 => L28 | L26 => L29 | L27 => L7 | L28 => L10 | L29 => L0 | L30 => L11 | L31 => L33 | L32 => L26 | L33 => L5 | L34 => L16 end.

(* P42 : S1 S13 S18 S28 S32 S47 S51 ->
   P44 : S1 S13 S19 S24 S37 S42 S54  *)
Definition fp42_44 (p:Point) := match p with P0 => P12 | P1 => P7 | P2 => P4 | P3 => P13 | P4 => P2 | P5 => P5 | P6 => P10 | P7 => P1 | P8 => P14 | P9 => P9 | P10 => P6 | P11 => P11 | P12 => P0 | P13 => P3 | P14 => P8 end.
Definition fl42_44 (l:Line) := match l with L0 => L26 | L1 => L16 | L2 => L30 | L3 => L9 | L4 => L33 | L5 => L5 | L6 => L20 | L7 => L13 | L8 => L31 | L9 => L3 | L10 => L10 | L11 => L22 | L12 => L28 | L13 => L7 | L14 => L24 | L15 => L25 | L16 => L1 | L17 => L17 | L18 => L23 | L19 => L32 | L20 => L6 | L21 => L21 | L22 => L11 | L23 => L18 | L24 => L14 | L25 => L15 | L26 => L0 | L27 => L27 | L28 => L12 | L29 => L29 | L30 => L2 | L31 => L8 | L32 => L19 | L33 => L4 | L34 => L34 end.

(* P44 : S1 S13 S19 S24 S37 S42 S54 ->
   P47 : S1 S13 S22 S30 S34 S43 S49  *)
Definition fp44_47 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl44_47 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P47 : S1 S13 S22 S30 S34 S43 S49 ->
   P48 : S1 S14 S17 S24 S34 S47 S53  *)
Definition fp47_48 (p:Point) := match p with P0 => P11 | P1 => P9 | P2 => P5 | P3 => P1 | P4 => P13 | P5 => P7 | P6 => P3 | P7 => P6 | P8 => P10 | P9 => P12 | P10 => P0 | P11 => P4 | P12 => P8 | P13 => P14 | P14 => P2 end.
Definition fl47_48 (l:Line) := match l with L0 => L29 | L1 => L11 | L2 => L22 | L3 => L34 | L4 => L5 | L5 => L24 | L6 => L14 | L7 => L21 | L8 => L4 | L9 => L18 | L10 => L33 | L11 => L23 | L12 => L10 | L13 => L2 | L14 => L17 | L15 => L12 | L16 => L27 | L17 => L28 | L18 => L30 | L19 => L0 | L20 => L8 | L21 => L9 | L22 => L7 | L23 => L16 | L24 => L25 | L25 => L6 | L26 => L32 | L27 => L13 | L28 => L31 | L29 => L26 | L30 => L3 | L31 => L15 | L32 => L19 | L33 => L20 | L34 => L1 end.

(* P48 : S1 S14 S17 S24 S34 S47 S53 ->
   P51 : S1 S14 S19 S31 S32 S43 S52  *)
Definition fp48_51 (p:Point) := match p with P0 => P10 | P1 => P14 | P2 => P3 | P3 => P7 | P4 => P2 | P5 => P6 | P6 => P11 | P7 => P0 | P8 => P9 | P9 => P13 | P10 => P4 | P11 => P8 | P12 => P1 | P13 => P5 | P14 => P12 end.
Definition fl48_51 (l:Line) := match l with L0 => L19 | L1 => L13 | L2 => L34 | L3 => L4 | L4 => L25 | L5 => L8 | L6 => L30 | L7 => L14 | L8 => L23 | L9 => L9 | L10 => L6 | L11 => L27 | L12 => L31 | L13 => L1 | L14 => L20 | L15 => L22 | L16 => L12 | L17 => L15 | L18 => L21 | L19 => L26 | L20 => L10 | L21 => L28 | L22 => L3 | L23 => L16 | L24 => L18 | L25 => L17 | L26 => L0 | L27 => L33 | L28 => L2 | L29 => L32 | L30 => L7 | L31 => L5 | L32 => L29 | L33 => L11 | L34 => L24 end.

(* P51 : S1 S14 S19 S31 S32 S43 S52 ->
   P52 : S1 S14 S20 S27 S39 S42 S49  *)
Definition fp51_52 (p:Point) := match p with P0 => P10 | P1 => P14 | P2 => P3 | P3 => P2 | P4 => P7 | P5 => P11 | P6 => P6 | P7 => P4 | P8 => P13 | P9 => P9 | P10 => P0 | P11 => P5 | P12 => P12 | P13 => P8 | P14 => P1 end.
Definition fl51_52 (l:Line) := match l with L0 => L19 | L1 => L13 | L2 => L34 | L3 => L25 | L4 => L4 | L5 => L30 | L6 => L8 | L7 => L31 | L8 => L6 | L9 => L9 | L10 => L23 | L11 => L27 | L12 => L14 | L13 => L1 | L14 => L12 | L15 => L15 | L16 => L20 | L17 => L22 | L18 => L21 | L19 => L0 | L20 => L16 | L21 => L18 | L22 => L17 | L23 => L10 | L24 => L28 | L25 => L3 | L26 => L26 | L27 => L11 | L28 => L24 | L29 => L29 | L30 => L5 | L31 => L7 | L32 => L32 | L33 => L33 | L34 => L2 end.

(* P52 : S1 S14 S20 S27 S39 S42 S49 ->
   P54 : S1 S15 S17 S27 S32 S44 S54  *)
Definition fp52_54 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P11 | P4 => P13 | P5 => P12 | P6 => P14 | P7 => P8 | P8 => P10 | P9 => P7 | P10 => P9 | P11 => P4 | P12 => P6 | P13 => P3 | P14 => P5 end.
Definition fl52_54 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L8 | L4 => L10 | L5 => L7 | L6 => L12 | L7 => L6 | L8 => L4 | L9 => L2 | L10 => L3 | L11 => L1 | L12 => L5 | L13 => L18 | L14 => L17 | L15 => L14 | L16 => L15 | L17 => L16 | L18 => L13 | L19 => L29 | L20 => L34 | L21 => L22 | L22 => L24 | L23 => L28 | L24 => L25 | L25 => L21 | L26 => L32 | L27 => L30 | L28 => L20 | L29 => L26 | L30 => L33 | L31 => L27 | L32 => L19 | L33 => L31 | L34 => L23 end.

(* P54 : S1 S15 S17 S27 S32 S44 S54 ->
   P56 : S1 S15 S18 S30 S33 S42 S53  *)
Definition fp54_56 (p:Point) := match p with P0 => P6 | P1 => P13 | P2 => P8 | P3 => P14 | P4 => P7 | P5 => P0 | P6 => P5 | P7 => P12 | P8 => P9 | P9 => P2 | P10 => P3 | P11 => P1 | P12 => P4 | P13 => P11 | P14 => P10 end.
Definition fl54_56 (l:Line) := match l with L0 => L32 | L1 => L31 | L2 => L2 | L3 => L33 | L4 => L15 | L5 => L7 | L6 => L34 | L7 => L28 | L8 => L21 | L9 => L25 | L10 => L16 | L11 => L11 | L12 => L6 | L13 => L20 | L14 => L8 | L15 => L27 | L16 => L24 | L17 => L3 | L18 => L18 | L19 => L19 | L20 => L23 | L21 => L14 | L22 => L9 | L23 => L13 | L24 => L10 | L25 => L22 | L26 => L26 | L27 => L4 | L28 => L5 | L29 => L0 | L30 => L1 | L31 => L30 | L32 => L29 | L33 => L17 | L34 => L12 end.

(* P56 : S1 S15 S18 S30 S33 S42 S53 ->
   P59 : S1 S15 S20 S31 S34 S40 S51  *)
Definition fp56_59 (p:Point) := match p with P0 => P6 | P1 => P8 | P2 => P13 | P3 => P7 | P4 => P14 | P5 => P0 | P6 => P5 | P7 => P10 | P8 => P11 | P9 => P1 | P10 => P4 | P11 => P2 | P12 => P3 | P13 => P9 | P14 => P12 end.
Definition fl56_59 (l:Line) := match l with L0 => L32 | L1 => L31 | L2 => L2 | L3 => L34 | L4 => L7 | L5 => L15 | L6 => L33 | L7 => L27 | L8 => L24 | L9 => L20 | L10 => L8 | L11 => L18 | L12 => L3 | L13 => L25 | L14 => L16 | L15 => L28 | L16 => L21 | L17 => L6 | L18 => L11 | L19 => L26 | L20 => L22 | L21 => L10 | L22 => L13 | L23 => L9 | L24 => L14 | L25 => L23 | L26 => L19 | L27 => L5 | L28 => L4 | L29 => L0 | L30 => L1 | L31 => L30 | L32 => L29 | L33 => L12 | L34 => L17 end.

(* P59 : S1 S15 S20 S31 S34 S40 S51 ->
   P61 : S2 S9 S18 S30 S36 S45 S49  *)
Definition fp59_61 (p:Point) := match p with P0 => P10 | P1 => P11 | P2 => P6 | P3 => P8 | P4 => P1 | P5 => P4 | P6 => P13 | P7 => P2 | P8 => P7 | P9 => P14 | P10 => P3 | P11 => P9 | P12 => P0 | P13 => P5 | P14 => P12 end.
Definition fl59_61 (l:Line) := match l with L0 => L34 | L1 => L8 | L2 => L25 | L3 => L13 | L4 => L19 | L5 => L4 | L6 => L30 | L7 => L11 | L8 => L22 | L9 => L5 | L10 => L14 | L11 => L29 | L12 => L24 | L13 => L15 | L14 => L33 | L15 => L32 | L16 => L2 | L17 => L7 | L18 => L31 | L19 => L20 | L20 => L3 | L21 => L27 | L22 => L18 | L23 => L9 | L24 => L10 | L25 => L12 | L26 => L0 | L27 => L26 | L28 => L17 | L29 => L23 | L30 => L1 | L31 => L16 | L32 => L28 | L33 => L6 | L34 => L21 end.

(* P61 : S2 S9 S18 S30 S36 S45 S49 ->
   P63 : S2 S9 S19 S29 S38 S40 S52  *)
Definition fp61_63 (p:Point) := match p with P0 => P12 | P1 => P8 | P2 => P3 | P3 => P2 | P4 => P13 | P5 => P9 | P6 => P6 | P7 => P14 | P8 => P1 | P9 => P5 | P10 => P10 | P11 => P11 | P12 => P0 | P13 => P4 | P14 => P7 end.
Definition fl61_63 (l:Line) := match l with L0 => L20 | L1 => L16 | L2 => L33 | L3 => L9 | L4 => L30 | L5 => L5 | L6 => L26 | L7 => L32 | L8 => L8 | L9 => L3 | L10 => L27 | L11 => L24 | L12 => L18 | L13 => L19 | L14 => L22 | L15 => L15 | L16 => L1 | L17 => L21 | L18 => L12 | L19 => L13 | L20 => L0 | L21 => L17 | L22 => L14 | L23 => L28 | L24 => L11 | L25 => L25 | L26 => L6 | L27 => L10 | L28 => L23 | L29 => L29 | L30 => L4 | L31 => L31 | L32 => L7 | L33 => L2 | L34 => L34 end.

(* P63 : S2 S9 S19 S29 S38 S40 S52 ->
   P64 : S2 S9 S23 S24 S35 S44 S54  *)
Definition fp63_64 (p:Point) := match p with P0 => P8 | P1 => P12 | P2 => P3 | P3 => P1 | P4 => P10 | P5 => P14 | P6 => P5 | P7 => P9 | P8 => P2 | P9 => P6 | P10 => P13 | P11 => P7 | P12 => P0 | P13 => P4 | P14 => P11 end.
Definition fl63_64 (l:Line) := match l with L0 => L20 | L1 => L8 | L2 => L27 | L3 => L18 | L4 => L32 | L5 => L3 | L6 => L24 | L7 => L30 | L8 => L16 | L9 => L5 | L10 => L33 | L11 => L26 | L12 => L9 | L13 => L21 | L14 => L22 | L15 => L12 | L16 => L1 | L17 => L19 | L18 => L15 | L19 => L11 | L20 => L0 | L21 => L7 | L22 => L10 | L23 => L34 | L24 => L13 | L25 => L25 | L26 => L4 | L27 => L14 | L28 => L23 | L29 => L31 | L30 => L6 | L31 => L29 | L32 => L17 | L33 => L2 | L34 => L28 end.

(* P64 : S2 S9 S23 S24 S35 S44 S54 ->
   P67 : S2 S10 S16 S29 S39 S44 S49  *)
Definition fp64_67 (p:Point) := match p with P0 => P7 | P1 => P13 | P2 => P5 | P3 => P10 | P4 => P2 | P5 => P4 | P6 => P12 | P7 => P14 | P8 => P6 | P9 => P0 | P10 => P8 | P11 => P3 | P12 => P11 | P13 => P9 | P14 => P1 end.
Definition fl64_67 (l:Line) := match l with L0 => L28 | L1 => L13 | L2 => L26 | L3 => L31 | L4 => L3 | L5 => L22 | L6 => L10 | L7 => L16 | L8 => L32 | L9 => L11 | L10 => L6 | L11 => L21 | L12 => L25 | L13 => L27 | L14 => L12 | L15 => L30 | L16 => L29 | L17 => L17 | L18 => L2 | L19 => L8 | L20 => L34 | L21 => L4 | L22 => L19 | L23 => L0 | L24 => L15 | L25 => L18 | L26 => L14 | L27 => L7 | L28 => L23 | L29 => L1 | L30 => L24 | L31 => L9 | L32 => L33 | L33 => L5 | L34 => L20 end.

(* P67 : S2 S10 S16 S29 S39 S44 S49 ->
   P68 : S2 S10 S21 S24 S36 S47 S51  *)
Definition fp67_68 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl67_68 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P68 : S2 S10 S21 S24 S36 S47 S51 ->
   P71 : S2 S10 S23 S30 S33 S43 S52  *)
Definition fp68_71 (p:Point) := match p with P0 => P4 | P1 => P14 | P2 => P9 | P3 => P3 | P4 => P0 | P5 => P10 | P6 => P13 | P7 => P11 | P8 => P8 | P9 => P2 | P10 => P5 | P11 => P7 | P12 => P12 | P13 => P6 | P14 => P1 end.
Definition fl68_71 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L24 | L4 => L17 | L5 => L26 | L6 => L7 | L7 => L6 | L8 => L27 | L9 => L9 | L10 => L14 | L11 => L31 | L12 => L19 | L13 => L29 | L14 => L10 | L15 => L21 | L16 => L33 | L17 => L4 | L18 => L18 | L19 => L12 | L20 => L20 | L21 => L15 | L22 => L22 | L23 => L0 | L24 => L3 | L25 => L2 | L26 => L5 | L27 => L8 | L28 => L34 | L29 => L13 | L30 => L30 | L31 => L11 | L32 => L32 | L33 => L16 | L34 => L28 end.

(* P71 : S2 S10 S23 S30 S33 S43 S52 ->
   P73 : S2 S12 S18 S29 S33 S47 S50  *)
Definition fp71_73 (p:Point) := match p with P0 => P10 | P1 => P6 | P2 => P11 | P3 => P5 | P4 => P12 | P5 => P0 | P6 => P9 | P7 => P2 | P8 => P7 | P9 => P3 | P10 => P14 | P11 => P4 | P12 => P13 | P13 => P1 | P14 => P8 end.
Definition fl71_73 (l:Line) := match l with L0 => L34 | L1 => L30 | L2 => L4 | L3 => L13 | L4 => L19 | L5 => L25 | L6 => L8 | L7 => L33 | L8 => L31 | L9 => L32 | L10 => L15 | L11 => L7 | L12 => L2 | L13 => L14 | L14 => L24 | L15 => L29 | L16 => L11 | L17 => L5 | L18 => L22 | L19 => L27 | L20 => L28 | L21 => L12 | L22 => L17 | L23 => L20 | L24 => L26 | L25 => L9 | L26 => L16 | L27 => L3 | L28 => L0 | L29 => L1 | L30 => L6 | L31 => L18 | L32 => L10 | L33 => L21 | L34 => L23 end.

(* P73 : S2 S12 S18 S29 S33 S47 S50 ->
   P74 : S2 S12 S19 S25 S36 S43 S54  *)
Definition fp73_74 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P11 | P4 => P14 | P5 => P13 | P6 => P12 | P7 => P7 | P8 => P10 | P9 => P9 | P10 => P8 | P11 => P3 | P12 => P6 | P13 => P5 | P14 => P4 end.
Definition fl73_74 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L13 | L4 => L18 | L5 => L15 | L6 => L17 | L7 => L9 | L8 => L8 | L9 => L7 | L10 => L10 | L11 => L12 | L12 => L11 | L13 => L3 | L14 => L1 | L15 => L5 | L16 => L2 | L17 => L6 | L18 => L4 | L19 => L24 | L20 => L34 | L21 => L29 | L22 => L22 | L23 => L23 | L24 => L19 | L25 => L27 | L26 => L31 | L27 => L25 | L28 => L28 | L29 => L21 | L30 => L32 | L31 => L26 | L32 => L30 | L33 => L33 | L34 => L20 end.

(* P74 : S2 S12 S19 S25 S36 S43 S54 ->
   P77 : S2 S12 S23 S26 S39 S40 S51  *)
Definition fp74_77 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P7 | P4 => P9 | P5 => P10 | P6 => P8 | P7 => P11 | P8 => P13 | P9 => P14 | P10 => P12 | P11 => P3 | P12 => P5 | P13 => P6 | P14 => P4 end.
Definition fl74_77 (l:Line) := match l with L0 => L0 | L1 => L10 | L2 => L8 | L3 => L11 | L4 => L9 | L5 => L12 | L6 => L7 | L7 => L18 | L8 => L16 | L9 => L17 | L10 => L14 | L11 => L15 | L12 => L13 | L13 => L5 | L14 => L1 | L15 => L3 | L16 => L2 | L17 => L4 | L18 => L6 | L19 => L26 | L20 => L28 | L21 => L31 | L22 => L22 | L23 => L23 | L24 => L21 | L25 => L33 | L26 => L29 | L27 => L25 | L28 => L34 | L29 => L19 | L30 => L30 | L31 => L24 | L32 => L32 | L33 => L27 | L34 => L20 end.

(* P77 : S2 S12 S23 S26 S39 S40 S51 ->
   P78 : S2 S14 S16 S25 S35 S47 S52  *)
Definition fp77_78 (p:Point) := match p with P0 => P12 | P1 => P8 | P2 => P3 | P3 => P6 | P4 => P9 | P5 => P13 | P6 => P2 | P7 => P5 | P8 => P10 | P9 => P14 | P10 => P1 | P11 => P0 | P12 => P11 | P13 => P7 | P14 => P4 end.
Definition fl77_78 (l:Line) := match l with L0 => L20 | L1 => L33 | L2 => L16 | L3 => L30 | L4 => L9 | L5 => L5 | L6 => L26 | L7 => L18 | L8 => L8 | L9 => L24 | L10 => L27 | L11 => L3 | L12 => L32 | L13 => L12 | L14 => L1 | L15 => L15 | L16 => L22 | L17 => L21 | L18 => L19 | L19 => L7 | L20 => L34 | L21 => L31 | L22 => L2 | L23 => L23 | L24 => L4 | L25 => L10 | L26 => L29 | L27 => L25 | L28 => L28 | L29 => L6 | L30 => L11 | L31 => L17 | L32 => L13 | L33 => L14 | L34 => L0 end.

(* P78 : S2 S14 S16 S25 S35 S47 S52 ->
   P80 : S2 S14 S19 S24 S39 S45 S50  *)
Definition fp78_80 (p:Point) := match p with P0 => P6 | P1 => P10 | P2 => P11 | P3 => P9 | P4 => P12 | P5 => P0 | P6 => P5 | P7 => P1 | P8 => P4 | P9 => P8 | P10 => P13 | P11 => P7 | P12 => P14 | P13 => P2 | P14 => P3 end.
Definition fl78_80 (l:Line) := match l with L0 => L34 | L1 => L33 | L2 => L2 | L3 => L7 | L4 => L32 | L5 => L31 | L6 => L15 | L7 => L30 | L8 => L25 | L9 => L19 | L10 => L8 | L11 => L13 | L12 => L4 | L13 => L11 | L14 => L22 | L15 => L29 | L16 => L14 | L17 => L5 | L18 => L24 | L19 => L21 | L20 => L23 | L21 => L18 | L22 => L10 | L23 => L20 | L24 => L26 | L25 => L16 | L26 => L9 | L27 => L1 | L28 => L0 | L29 => L3 | L30 => L6 | L31 => L12 | L32 => L17 | L33 => L27 | L34 => L28 end.

(* P80 : S2 S14 S19 S24 S39 S45 S50 ->
   P83 : S2 S14 S21 S26 S38 S43 S49  *)
Definition fp80_83 (p:Point) := match p with P0 => P6 | P1 => P11 | P2 => P10 | P3 => P12 | P4 => P9 | P5 => P0 | P6 => P5 | P7 => P2 | P8 => P3 | P9 => P14 | P10 => P7 | P11 => P13 | P12 => P8 | P13 => P1 | P14 => P4 end.
Definition fl80_83 (l:Line) := match l with L0 => L34 | L1 => L33 | L2 => L2 | L3 => L15 | L4 => L31 | L5 => L32 | L6 => L7 | L7 => L29 | L8 => L22 | L9 => L24 | L10 => L14 | L11 => L11 | L12 => L5 | L13 => L13 | L14 => L25 | L15 => L30 | L16 => L8 | L17 => L4 | L18 => L19 | L19 => L26 | L20 => L20 | L21 => L9 | L22 => L16 | L23 => L23 | L24 => L21 | L25 => L10 | L26 => L18 | L27 => L1 | L28 => L0 | L29 => L6 | L30 => L3 | L31 => L17 | L32 => L12 | L33 => L27 | L34 => L28 end.

(* P83 : S2 S14 S21 S26 S38 S43 S49 ->
   P85 : S2 S15 S16 S26 S33 S45 S54  *)
Definition fp83_85 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P11 | P4 => P13 | P5 => P12 | P6 => P14 | P7 => P8 | P8 => P10 | P9 => P7 | P10 => P9 | P11 => P4 | P12 => P6 | P13 => P3 | P14 => P5 end.
Definition fl83_85 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L8 | L4 => L10 | L5 => L7 | L6 => L12 | L7 => L6 | L8 => L4 | L9 => L2 | L10 => L3 | L11 => L1 | L12 => L5 | L13 => L18 | L14 => L17 | L15 => L14 | L16 => L15 | L17 => L16 | L18 => L13 | L19 => L29 | L20 => L34 | L21 => L22 | L22 => L24 | L23 => L28 | L24 => L25 | L25 => L21 | L26 => L32 | L27 => L30 | L28 => L20 | L29 => L26 | L30 => L33 | L31 => L27 | L32 => L19 | L33 => L31 | L34 => L23 end.

(* P85 : S2 S15 S16 S26 S33 S45 S54 ->
   P86 : S2 S15 S18 S25 S38 S44 S51  *)
Definition fp85_86 (p:Point) := match p with P0 => P9 | P1 => P14 | P2 => P4 | P3 => P8 | P4 => P2 | P5 => P5 | P6 => P11 | P7 => P13 | P8 => P3 | P9 => P0 | P10 => P10 | P11 => P6 | P12 => P12 | P13 => P7 | P14 => P1 end.
Definition fl85_86 (l:Line) := match l with L0 => L23 | L1 => L18 | L2 => L29 | L3 => L21 | L4 => L4 | L5 => L33 | L6 => L10 | L7 => L14 | L8 => L19 | L9 => L9 | L10 => L6 | L11 => L31 | L12 => L27 | L13 => L25 | L14 => L7 | L15 => L24 | L16 => L26 | L17 => L17 | L18 => L1 | L19 => L8 | L20 => L20 | L21 => L3 | L22 => L32 | L23 => L0 | L24 => L15 | L25 => L13 | L26 => L16 | L27 => L12 | L28 => L28 | L29 => L2 | L30 => L30 | L31 => L11 | L32 => L22 | L33 => L5 | L34 => L34 end.

(* P86 : S2 S15 S18 S25 S38 S44 S51 ->
   P89 : S2 S15 S21 S30 S35 S40 S50  *)
Definition fp86_89 (p:Point) := match p with P0 => P8 | P1 => P12 | P2 => P3 | P3 => P9 | P4 => P2 | P5 => P6 | P6 => P13 | P7 => P11 | P8 => P4 | P9 => P0 | P10 => P7 | P11 => P5 | P12 => P14 | P13 => P10 | P14 => P1 end.
Definition fl86_89 (l:Line) := match l with L0 => L20 | L1 => L18 | L2 => L32 | L3 => L24 | L4 => L3 | L5 => L27 | L6 => L8 | L7 => L16 | L8 => L26 | L9 => L9 | L10 => L5 | L11 => L30 | L12 => L33 | L13 => L22 | L14 => L12 | L15 => L21 | L16 => L19 | L17 => L15 | L18 => L1 | L19 => L10 | L20 => L23 | L21 => L4 | L22 => L29 | L23 => L0 | L24 => L17 | L25 => L13 | L26 => L14 | L27 => L7 | L28 => L34 | L29 => L2 | L30 => L31 | L31 => L11 | L32 => L25 | L33 => L6 | L34 => L28 end.

(* P89 : S2 S15 S21 S30 S35 S40 S50 ->
   P90 : S3 S8 S18 S28 S33 S45 S55  *)
Definition fp89_90 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P7 | P8 => P8 | P9 => P10 | P10 => P9 | P11 => P11 | P12 => P12 | P13 => P14 | P14 => P13 end.
Definition fl89_90 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L3 | L4 => L4 | L5 => L5 | L6 => L6 | L7 => L17 | L8 => L18 | L9 => L16 | L10 => L13 | L11 => L14 | L12 => L15 | L13 => L10 | L14 => L11 | L15 => L12 | L16 => L9 | L17 => L7 | L18 => L8 | L19 => L21 | L20 => L20 | L21 => L19 | L22 => L22 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L32 | L28 => L31 | L29 => L34 | L30 => L33 | L31 => L28 | L32 => L27 | L33 => L30 | L34 => L29 end.

(* P90 : S3 S8 S18 S28 S33 S45 S55 ->
   P92 : S3 S8 S21 S27 S36 S46 S49  *)
Definition fp90_92 (p:Point) := match p with P0 => P10 | P1 => P4 | P2 => P13 | P3 => P1 | P4 => P8 | P5 => P6 | P6 => P11 | P7 => P9 | P8 => P0 | P9 => P14 | P10 => P3 | P11 => P7 | P12 => P2 | P13 => P12 | P14 => P5 end.
Definition fl90_92 (l:Line) := match l with L0 => L25 | L1 => L8 | L2 => L34 | L3 => L4 | L4 => L19 | L5 => L13 | L6 => L30 | L7 => L24 | L8 => L1 | L9 => L17 | L10 => L23 | L11 => L26 | L12 => L7 | L13 => L21 | L14 => L28 | L15 => L11 | L16 => L16 | L17 => L32 | L18 => L6 | L19 => L12 | L20 => L0 | L21 => L9 | L22 => L10 | L23 => L27 | L24 => L3 | L25 => L20 | L26 => L18 | L27 => L2 | L28 => L33 | L29 => L31 | L30 => L15 | L31 => L29 | L32 => L5 | L33 => L14 | L34 => L22 end.

(* P92 : S3 S8 S21 S27 S36 S46 S49 ->
   P95 : S3 S8 S23 S31 S35 S40 S52  *)
Definition fp92_95 (p:Point) := match p with P0 => P10 | P1 => P4 | P2 => P13 | P3 => P8 | P4 => P1 | P5 => P11 | P6 => P6 | P7 => P14 | P8 => P3 | P9 => P9 | P10 => P0 | P11 => P5 | P12 => P12 | P13 => P2 | P14 => P7 end.
Definition fl92_95 (l:Line) := match l with L0 => L25 | L1 => L8 | L2 => L34 | L3 => L19 | L4 => L4 | L5 => L30 | L6 => L13 | L7 => L7 | L8 => L1 | L9 => L26 | L10 => L23 | L11 => L17 | L12 => L24 | L13 => L6 | L14 => L28 | L15 => L32 | L16 => L16 | L17 => L11 | L18 => L21 | L19 => L3 | L20 => L20 | L21 => L18 | L22 => L27 | L23 => L10 | L24 => L12 | L25 => L0 | L26 => L9 | L27 => L22 | L28 => L14 | L29 => L29 | L30 => L5 | L31 => L31 | L32 => L15 | L33 => L33 | L34 => L2 end.

(* P95 : S3 S8 S23 S31 S35 S40 S52 ->
   P97 : S3 S11 S16 S29 S33 S46 S52  *)
Definition fp95_97 (p:Point) := match p with P0 => P10 | P1 => P13 | P2 => P4 | P3 => P6 | P4 => P11 | P5 => P8 | P6 => P1 | P7 => P2 | P8 => P7 | P9 => P12 | P10 => P5 | P11 => P3 | P12 => P14 | P13 => P9 | P14 => P0 end.
Definition fl95_97 (l:Line) := match l with L0 => L25 | L1 => L34 | L2 => L8 | L3 => L13 | L4 => L30 | L5 => L19 | L6 => L4 | L7 => L11 | L8 => L28 | L9 => L6 | L10 => L16 | L11 => L21 | L12 => L32 | L13 => L17 | L14 => L1 | L15 => L7 | L16 => L23 | L17 => L24 | L18 => L26 | L19 => L2 | L20 => L31 | L21 => L33 | L22 => L15 | L23 => L5 | L24 => L22 | L25 => L29 | L26 => L14 | L27 => L3 | L28 => L18 | L29 => L20 | L30 => L27 | L31 => L0 | L32 => L10 | L33 => L9 | L34 => L12 end.

(* P97 : S3 S11 S16 S29 S33 S46 S52 ->
   P98 : S3 S11 S17 S24 S36 S45 S54  *)
Definition fp97_98 (p:Point) := match p with P0 => P12 | P1 => P8 | P2 => P3 | P3 => P1 | P4 => P14 | P5 => P10 | P6 => P5 | P7 => P11 | P8 => P0 | P9 => P4 | P10 => P7 | P11 => P13 | P12 => P2 | P13 => P6 | P14 => P9 end.
Definition fl97_98 (l:Line) := match l with L0 => L20 | L1 => L9 | L2 => L30 | L3 => L5 | L4 => L26 | L5 => L16 | L6 => L33 | L7 => L27 | L8 => L3 | L9 => L18 | L10 => L24 | L11 => L32 | L12 => L8 | L13 => L22 | L14 => L21 | L15 => L12 | L16 => L15 | L17 => L19 | L18 => L1 | L19 => L10 | L20 => L0 | L21 => L7 | L22 => L11 | L23 => L23 | L24 => L6 | L25 => L31 | L26 => L14 | L27 => L4 | L28 => L34 | L29 => L25 | L30 => L13 | L31 => L29 | L32 => L2 | L33 => L17 | L34 => L28 end.

(* P98 : S3 S11 S17 S24 S36 S45 S54 ->
   P101 : S3 S11 S21 S28 S38 S40 S51  *)
Definition fp98_101 (p:Point) := match p with P0 => P12 | P1 => P3 | P2 => P8 | P3 => P1 | P4 => P14 | P5 => P5 | P6 => P10 | P7 => P13 | P8 => P2 | P9 => P9 | P10 => P6 | P11 => P11 | P12 => P0 | P13 => P7 | P14 => P4 end.
Definition fl98_101 (l:Line) := match l with L0 => L20 | L1 => L9 | L2 => L30 | L3 => L16 | L4 => L33 | L5 => L5 | L6 => L26 | L7 => L19 | L8 => L15 | L9 => L1 | L10 => L21 | L11 => L22 | L12 => L12 | L13 => L32 | L14 => L24 | L15 => L8 | L16 => L3 | L17 => L27 | L18 => L18 | L19 => L7 | L20 => L0 | L21 => L10 | L22 => L11 | L23 => L23 | L24 => L14 | L25 => L31 | L26 => L6 | L27 => L17 | L28 => L28 | L29 => L29 | L30 => L2 | L31 => L25 | L32 => L13 | L33 => L4 | L34 => L34 end.

(* P101 : S3 S11 S21 S28 S38 S40 S51 ->
   P103 : S3 S12 S17 S29 S34 S40 S55  *)
Definition fp101_103 (p:Point) := match p with P0 => P13 | P1 => P4 | P2 => P10 | P3 => P8 | P4 => P6 | P5 => P11 | P6 => P1 | P7 => P2 | P8 => P12 | P9 => P5 | P10 => P7 | P11 => P9 | P12 => P3 | P13 => P14 | P14 => P0 end.
Definition fl101_103 (l:Line) := match l with L0 => L25 | L1 => L32 | L2 => L11 | L3 => L16 | L4 => L28 | L5 => L21 | L6 => L6 | L7 => L7 | L8 => L26 | L9 => L1 | L10 => L17 | L11 => L23 | L12 => L24 | L13 => L13 | L14 => L4 | L15 => L8 | L16 => L19 | L17 => L34 | L18 => L30 | L19 => L3 | L20 => L20 | L21 => L27 | L22 => L18 | L23 => L2 | L24 => L33 | L25 => L31 | L26 => L15 | L27 => L5 | L28 => L14 | L29 => L29 | L30 => L22 | L31 => L0 | L32 => L9 | L33 => L12 | L34 => L10 end.

(* P103 : S3 S12 S17 S29 S34 S40 S55 ->
   P105 : S3 S12 S18 S31 S36 S41 S51  *)
Definition fp103_105 (p:Point) := match p with P0 => P5 | P1 => P9 | P2 => P11 | P3 => P12 | P4 => P10 | P5 => P6 | P6 => P0 | P7 => P1 | P8 => P3 | P9 => P7 | P10 => P13 | P11 => P14 | P12 => P8 | P13 => P4 | P14 => P2 end.
Definition fl103_105 (l:Line) := match l with L0 => L29 | L1 => L30 | L2 => L2 | L3 => L12 | L4 => L28 | L5 => L27 | L6 => L17 | L7 => L4 | L8 => L21 | L9 => L18 | L10 => L10 | L11 => L23 | L12 => L33 | L13 => L11 | L14 => L14 | L15 => L5 | L16 => L24 | L17 => L34 | L18 => L22 | L19 => L16 | L20 => L20 | L21 => L26 | L22 => L9 | L23 => L13 | L24 => L19 | L25 => L25 | L26 => L8 | L27 => L15 | L28 => L7 | L29 => L31 | L30 => L32 | L31 => L0 | L32 => L1 | L33 => L3 | L34 => L6 end.

(* P105 : S3 S12 S18 S31 S36 S41 S51 ->
   P106 : S3 S12 S23 S27 S33 S42 S54  *)
Definition fp105_106 (p:Point) := match p with P0 => P5 | P1 => P11 | P2 => P9 | P3 => P10 | P4 => P12 | P5 => P6 | P6 => P0 | P7 => P2 | P8 => P4 | P9 => P14 | P10 => P8 | P11 => P7 | P12 => P13 | P13 => P3 | P14 => P1 end.
Definition fl105_106 (l:Line) := match l with L0 => L29 | L1 => L30 | L2 => L2 | L3 => L17 | L4 => L27 | L5 => L28 | L6 => L12 | L7 => L5 | L8 => L24 | L9 => L11 | L10 => L14 | L11 => L22 | L12 => L34 | L13 => L18 | L14 => L10 | L15 => L4 | L16 => L21 | L17 => L33 | L18 => L23 | L19 => L8 | L20 => L25 | L21 => L19 | L22 => L13 | L23 => L9 | L24 => L26 | L25 => L20 | L26 => L16 | L27 => L7 | L28 => L15 | L29 => L31 | L30 => L32 | L31 => L0 | L32 => L1 | L33 => L6 | L34 => L3 end.

(* P106 : S3 S12 S23 S27 S33 S42 S54 ->
   P108 : S3 S13 S16 S28 S35 S41 S54  *)
Definition fp106_108 (p:Point) := match p with P0 => P8 | P1 => P3 | P2 => P12 | P3 => P14 | P4 => P5 | P5 => P10 | P6 => P1 | P7 => P0 | P8 => P7 | P9 => P4 | P10 => P11 | P11 => P13 | P12 => P6 | P13 => P9 | P14 => P2 end.
Definition fl106_108 (l:Line) := match l with L0 => L20 | L1 => L27 | L2 => L8 | L3 => L3 | L4 => L24 | L5 => L32 | L6 => L18 | L7 => L12 | L8 => L22 | L9 => L15 | L10 => L1 | L11 => L21 | L12 => L19 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L33 | L17 => L30 | L18 => L26 | L19 => L14 | L20 => L31 | L21 => L23 | L22 => L6 | L23 => L17 | L24 => L28 | L25 => L29 | L26 => L2 | L27 => L13 | L28 => L4 | L29 => L25 | L30 => L34 | L31 => L0 | L32 => L10 | L33 => L7 | L34 => L11 end.

(* P108 : S3 S13 S16 S28 S35 S41 S54 ->
   P111 : S3 S13 S18 S29 S38 S42 S49  *)
Definition fp108_111 (p:Point) := match p with P0 => P4 | P1 => P10 | P2 => P13 | P3 => P3 | P4 => P0 | P5 => P14 | P6 => P9 | P7 => P11 | P8 => P8 | P9 => P6 | P10 => P1 | P11 => P7 | P12 => P12 | P13 => P2 | P14 => P5 end.
Definition fl108_111 (l:Line) := match l with L0 => L25 | L1 => L1 | L2 => L23 | L3 => L24 | L4 => L7 | L5 => L26 | L6 => L17 | L7 => L4 | L8 => L8 | L9 => L30 | L10 => L34 | L11 => L13 | L12 => L19 | L13 => L11 | L14 => L28 | L15 => L21 | L16 => L16 | L17 => L6 | L18 => L32 | L19 => L12 | L20 => L20 | L21 => L15 | L22 => L22 | L23 => L2 | L24 => L3 | L25 => L0 | L26 => L5 | L27 => L27 | L28 => L14 | L29 => L31 | L30 => L9 | L31 => L29 | L32 => L18 | L33 => L33 | L34 => L10 end.

(* P111 : S3 S13 S18 S29 S38 S42 S49 ->
   P112 : S3 S13 S23 S24 S34 S46 S51  *)
Definition fp111_112 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl111_112 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P112 : S3 S13 S23 S24 S34 S46 S51 ->
   P114 : S3 S14 S16 S31 S34 S45 S49  *)
Definition fp112_114 (p:Point) := match p with P0 => P8 | P1 => P3 | P2 => P12 | P3 => P14 | P4 => P5 | P5 => P10 | P6 => P1 | P7 => P0 | P8 => P7 | P9 => P4 | P10 => P11 | P11 => P13 | P12 => P6 | P13 => P9 | P14 => P2 end.
Definition fl112_114 (l:Line) := match l with L0 => L20 | L1 => L27 | L2 => L8 | L3 => L3 | L4 => L24 | L5 => L32 | L6 => L18 | L7 => L12 | L8 => L22 | L9 => L15 | L10 => L1 | L11 => L21 | L12 => L19 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L33 | L17 => L30 | L18 => L26 | L19 => L14 | L20 => L31 | L21 => L23 | L22 => L6 | L23 => L17 | L24 => L28 | L25 => L29 | L26 => L2 | L27 => L13 | L28 => L4 | L29 => L25 | L30 => L34 | L31 => L0 | L32 => L10 | L33 => L7 | L34 => L11 end.

(* P114 : S3 S14 S16 S31 S34 S45 S49 ->
   P117 : S3 S14 S17 S27 S38 S41 S52  *)
Definition fp114_117 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P11 | P4 => P13 | P5 => P14 | P6 => P12 | P7 => P3 | P8 => P5 | P9 => P6 | P10 => P4 | P11 => P7 | P12 => P9 | P13 => P10 | P14 => P8 end.
Definition fl114_117 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L12 | L4 => L7 | L5 => L10 | L6 => L8 | L7 => L16 | L8 => L17 | L9 => L18 | L10 => L15 | L11 => L13 | L12 => L14 | L13 => L1 | L14 => L3 | L15 => L5 | L16 => L4 | L17 => L6 | L18 => L2 | L19 => L24 | L20 => L29 | L21 => L34 | L22 => L22 | L23 => L32 | L24 => L28 | L25 => L25 | L26 => L21 | L27 => L27 | L28 => L19 | L29 => L31 | L30 => L23 | L31 => L20 | L32 => L30 | L33 => L33 | L34 => L26 end.

(* P117 : S3 S14 S17 S27 S38 S41 S52 ->
   P118 : S3 S14 S21 S24 S35 S42 S55  *)
Definition fp117_118 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P11 | P4 => P13 | P5 => P12 | P6 => P14 | P7 => P7 | P8 => P9 | P9 => P8 | P10 => P10 | P11 => P3 | P12 => P5 | P13 => P4 | P14 => P6 end.
Definition fl117_118 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L10 | L4 => L8 | L5 => L12 | L6 => L7 | L7 => L6 | L8 => L4 | L9 => L2 | L10 => L3 | L11 => L1 | L12 => L5 | L13 => L13 | L14 => L15 | L15 => L14 | L16 => L17 | L17 => L16 | L18 => L18 | L19 => L34 | L20 => L29 | L21 => L24 | L22 => L22 | L23 => L32 | L24 => L21 | L25 => L25 | L26 => L28 | L27 => L33 | L28 => L26 | L29 => L20 | L30 => L30 | L31 => L31 | L32 => L23 | L33 => L27 | L34 => L19 end.

(* P118 : S3 S14 S21 S24 S35 S42 S55 ->
   P121 : S4 S8 S19 S31 S36 S45 S48  *)
Definition fp118_121 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P3 | P4 => P4 | P5 => P5 | P6 => P6 | P7 => P14 | P8 => P13 | P9 => P12 | P10 => P11 | P11 => P10 | P12 => P9 | P13 => P8 | P14 => P7 end.
Definition fl118_121 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L6 | L4 => L5 | L5 => L4 | L6 => L3 | L7 => L7 | L8 => L11 | L9 => L10 | L10 => L9 | L11 => L8 | L12 => L12 | L13 => L14 | L14 => L13 | L15 => L15 | L16 => L18 | L17 => L17 | L18 => L16 | L19 => L22 | L20 => L21 | L21 => L20 | L22 => L19 | L23 => L26 | L24 => L25 | L25 => L24 | L26 => L23 | L27 => L28 | L28 => L27 | L29 => L30 | L30 => L29 | L31 => L31 | L32 => L32 | L33 => L33 | L34 => L34 end.

(* P121 : S4 S8 S19 S31 S36 S45 S48 ->
   P122 : S4 S8 S22 S25 S35 S44 S55  *)
Definition fp121_122 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl121_122 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P122 : S4 S8 S22 S25 S35 S44 S55 ->
   P124 : S4 S8 S23 S26 S33 S46 S53  *)
Definition fp122_124 (p:Point) := match p with P0 => P11 | P1 => P8 | P2 => P4 | P3 => P14 | P4 => P2 | P5 => P5 | P6 => P9 | P7 => P13 | P8 => P1 | P9 => P6 | P10 => P10 | P11 => P0 | P12 => P12 | P13 => P7 | P14 => P3 end.
Definition fl122_124 (l:Line) := match l with L0 => L24 | L1 => L14 | L2 => L29 | L3 => L11 | L4 => L34 | L5 => L5 | L6 => L22 | L7 => L18 | L8 => L8 | L9 => L20 | L10 => L32 | L11 => L3 | L12 => L27 | L13 => L25 | L14 => L1 | L15 => L23 | L16 => L26 | L17 => L17 | L18 => L7 | L19 => L19 | L20 => L9 | L21 => L31 | L22 => L6 | L23 => L15 | L24 => L0 | L25 => L13 | L26 => L16 | L27 => L12 | L28 => L28 | L29 => L2 | L30 => L30 | L31 => L21 | L32 => L10 | L33 => L33 | L34 => L4 end.

(* P124 : S4 S8 S23 S26 S33 S46 S53 ->
   P127 : S4 S10 S17 S30 S36 S41 S53  *)
Definition fp124_127 (p:Point) := match p with P0 => P13 | P1 => P3 | P2 => P9 | P3 => P6 | P4 => P8 | P5 => P2 | P6 => P12 | P7 => P10 | P8 => P4 | P9 => P14 | P10 => P0 | P11 => P11 | P12 => P1 | P13 => P7 | P14 => P5 end.
Definition fl124_127 (l:Line) := match l with L0 => L21 | L1 => L32 | L2 => L16 | L3 => L25 | L4 => L6 | L5 => L11 | L6 => L28 | L7 => L20 | L8 => L1 | L9 => L12 | L10 => L19 | L11 => L22 | L12 => L15 | L13 => L4 | L14 => L29 | L15 => L33 | L16 => L10 | L17 => L18 | L18 => L23 | L19 => L2 | L20 => L7 | L21 => L31 | L22 => L34 | L23 => L27 | L24 => L24 | L25 => L3 | L26 => L8 | L27 => L17 | L28 => L13 | L29 => L14 | L30 => L0 | L31 => L30 | L32 => L26 | L33 => L9 | L34 => L5 end.

(* P127 : S4 S10 S17 S30 S36 S41 S53 ->
   P128 : S4 S10 S20 S29 S33 S42 S55  *)
Definition fp127_128 (p:Point) := match p with P0 => P6 | P1 => P7 | P2 => P14 | P3 => P8 | P4 => P13 | P5 => P0 | P6 => P5 | P7 => P12 | P8 => P9 | P9 => P4 | P10 => P1 | P11 => P3 | P12 => P2 | P13 => P11 | P14 => P10 end.
Definition fl127_128 (l:Line) := match l with L0 => L31 | L1 => L32 | L2 => L2 | L3 => L33 | L4 => L7 | L5 => L15 | L6 => L34 | L7 => L28 | L8 => L10 | L9 => L13 | L10 => L26 | L11 => L22 | L12 => L3 | L13 => L9 | L14 => L19 | L15 => L27 | L16 => L14 | L17 => L6 | L18 => L23 | L19 => L8 | L20 => L18 | L21 => L24 | L22 => L20 | L23 => L25 | L24 => L21 | L25 => L11 | L26 => L16 | L27 => L4 | L28 => L5 | L29 => L1 | L30 => L0 | L31 => L30 | L32 => L29 | L33 => L17 | L34 => L12 end.

(* P128 : S4 S10 S20 S29 S33 S42 S55 ->
   P131 : S4 S10 S23 S31 S32 S44 S51  *)
Definition fp128_131 (p:Point) := match p with P0 => P6 | P1 => P14 | P2 => P7 | P3 => P13 | P4 => P8 | P5 => P0 | P6 => P5 | P7 => P10 | P8 => P11 | P9 => P3 | P10 => P2 | P11 => P4 | P12 => P1 | P13 => P9 | P14 => P12 end.
Definition fl128_131 (l:Line) := match l with L0 => L31 | L1 => L32 | L2 => L2 | L3 => L34 | L4 => L15 | L5 => L7 | L6 => L33 | L7 => L27 | L8 => L14 | L9 => L9 | L10 => L19 | L11 => L23 | L12 => L6 | L13 => L13 | L14 => L26 | L15 => L28 | L16 => L10 | L17 => L3 | L18 => L22 | L19 => L16 | L20 => L11 | L21 => L21 | L22 => L25 | L23 => L20 | L24 => L24 | L25 => L18 | L26 => L8 | L27 => L5 | L28 => L4 | L29 => L1 | L30 => L0 | L31 => L30 | L32 => L29 | L33 => L12 | L34 => L17 end.

(* P131 : S4 S10 S23 S31 S32 S44 S51 ->
   P132 : S4 S11 S17 S29 S38 S44 S48  *)
Definition fp131_132 (p:Point) := match p with P0 => P13 | P1 => P3 | P2 => P9 | P3 => P7 | P4 => P5 | P5 => P11 | P6 => P1 | P7 => P2 | P8 => P12 | P9 => P6 | P10 => P8 | P11 => P10 | P12 => P4 | P13 => P14 | P14 => P0 end.
Definition fl131_132 (l:Line) := match l with L0 => L21 | L1 => L28 | L2 => L11 | L3 => L16 | L4 => L32 | L5 => L25 | L6 => L6 | L7 => L12 | L8 => L20 | L9 => L1 | L10 => L15 | L11 => L19 | L12 => L22 | L13 => L18 | L14 => L4 | L15 => L10 | L16 => L23 | L17 => L29 | L18 => L33 | L19 => L3 | L20 => L26 | L21 => L31 | L22 => L13 | L23 => L2 | L24 => L30 | L25 => L27 | L26 => L17 | L27 => L5 | L28 => L14 | L29 => L34 | L30 => L24 | L31 => L0 | L32 => L9 | L33 => L7 | L34 => L8 end.

(* P132 : S4 S11 S17 S29 S38 S44 S48 ->
   P134 : S4 S11 S20 S25 S36 S46 S51  *)
Definition fp132_134 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl132_134 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P134 : S4 S11 S20 S25 S36 S46 S51 ->
   P137 : S4 S11 S22 S30 S33 S45 S50  *)
Definition fp134_137 (p:Point) := match p with P0 => P9 | P1 => P13 | P2 => P3 | P3 => P8 | P4 => P2 | P5 => P6 | P6 => P12 | P7 => P10 | P8 => P0 | P9 => P4 | P10 => P14 | P11 => P1 | P12 => P7 | P13 => P11 | P14 => P5 end.
Definition fl134_137 (l:Line) := match l with L0 => L21 | L1 => L18 | L2 => L33 | L3 => L4 | L4 => L23 | L5 => L10 | L6 => L29 | L7 => L16 | L8 => L6 | L9 => L28 | L10 => L25 | L11 => L11 | L12 => L32 | L13 => L19 | L14 => L12 | L15 => L20 | L16 => L22 | L17 => L15 | L18 => L1 | L19 => L27 | L20 => L3 | L21 => L24 | L22 => L8 | L23 => L17 | L24 => L0 | L25 => L14 | L26 => L13 | L27 => L2 | L28 => L34 | L29 => L7 | L30 => L31 | L31 => L30 | L32 => L5 | L33 => L26 | L34 => L9 end.

(* P137 : S4 S11 S22 S30 S33 S45 S50 ->
   P138 : S4 S13 S19 S29 S32 S46 S50  *)
Definition fp137_138 (p:Point) := match p with P0 => P6 | P1 => P7 | P2 => P14 | P3 => P11 | P4 => P10 | P5 => P3 | P6 => P2 | P7 => P0 | P8 => P5 | P9 => P8 | P10 => P13 | P11 => P12 | P12 => P9 | P13 => P4 | P14 => P1 end.
Definition fl137_138 (l:Line) := match l with L0 => L31 | L1 => L34 | L2 => L15 | L3 => L2 | L4 => L32 | L5 => L33 | L6 => L7 | L7 => L13 | L8 => L28 | L9 => L10 | L10 => L3 | L11 => L26 | L12 => L22 | L13 => L6 | L14 => L9 | L15 => L14 | L16 => L23 | L17 => L19 | L18 => L27 | L19 => L11 | L20 => L29 | L21 => L24 | L22 => L5 | L23 => L8 | L24 => L30 | L25 => L25 | L26 => L4 | L27 => L12 | L28 => L1 | L29 => L20 | L30 => L21 | L31 => L0 | L32 => L17 | L33 => L18 | L34 => L16 end.

(* P138 : S4 S13 S19 S29 S32 S46 S50 ->
   P140 : S4 S13 S22 S26 S38 S41 S51  *)
Definition fp138_140 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl138_140 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P140 : S4 S13 S22 S26 S38 S41 S51 ->
   P143 : S4 S13 S23 S30 S35 S42 S48  *)
Definition fp140_143 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P13 | P4 => P12 | P5 => P11 | P6 => P14 | P7 => P7 | P8 => P10 | P9 => P9 | P10 => P8 | P11 => P5 | P12 => P4 | P13 => P3 | P14 => P6 end.
Definition fl140_143 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L13 | L4 => L18 | L5 => L17 | L6 => L15 | L7 => L9 | L8 => L8 | L9 => L7 | L10 => L10 | L11 => L12 | L12 => L11 | L13 => L3 | L14 => L2 | L15 => L6 | L16 => L1 | L17 => L5 | L18 => L4 | L19 => L32 | L20 => L25 | L21 => L21 | L22 => L28 | L23 => L33 | L24 => L30 | L25 => L20 | L26 => L26 | L27 => L34 | L28 => L22 | L29 => L29 | L30 => L24 | L31 => L31 | L32 => L19 | L33 => L23 | L34 => L27 end.

(* P143 : S4 S13 S23 S30 S35 S42 S48 ->
   P144 : S4 S14 S17 S26 S32 S45 S55  *)
Definition fp143_144 (p:Point) := match p with P0 => P14 | P1 => P6 | P2 => P7 | P3 => P5 | P4 => P8 | P5 => P0 | P6 => P13 | P7 => P9 | P8 => P4 | P9 => P12 | P10 => P1 | P11 => P11 | P12 => P2 | P13 => P10 | P14 => P3 end.
Definition fl143_144 (l:Line) := match l with L0 => L31 | L1 => L27 | L2 => L6 | L3 => L23 | L4 => L9 | L5 => L14 | L6 => L19 | L7 => L32 | L8 => L7 | L9 => L15 | L10 => L33 | L11 => L34 | L12 => L2 | L13 => L10 | L14 => L22 | L15 => L28 | L16 => L13 | L17 => L3 | L18 => L26 | L19 => L12 | L20 => L17 | L21 => L30 | L22 => L29 | L23 => L20 | L24 => L24 | L25 => L8 | L26 => L18 | L27 => L1 | L28 => L4 | L29 => L5 | L30 => L0 | L31 => L21 | L32 => L25 | L33 => L16 | L34 => L11 end.

(* P144 : S4 S14 S17 S26 S32 S45 S55 ->
   P146 : S4 S14 S19 S25 S38 S42 S53  *)
Definition fp144_146 (p:Point) := match p with P0 => P3 | P1 => P13 | P2 => P9 | P3 => P4 | P4 => P0 | P5 => P10 | P6 => P14 | P7 => P6 | P8 => P2 | P9 => P8 | P10 => P12 | P11 => P1 | P12 => P5 | P13 => P11 | P14 => P7 end.
Definition fl144_146 (l:Line) := match l with L0 => L21 | L1 => L1 | L2 => L19 | L3 => L15 | L4 => L20 | L5 => L12 | L6 => L22 | L7 => L6 | L8 => L16 | L9 => L28 | L10 => L32 | L11 => L11 | L12 => L25 | L13 => L33 | L14 => L10 | L15 => L23 | L16 => L29 | L17 => L4 | L18 => L18 | L19 => L26 | L20 => L17 | L21 => L24 | L22 => L7 | L23 => L3 | L24 => L0 | L25 => L5 | L26 => L2 | L27 => L13 | L28 => L34 | L29 => L8 | L30 => L30 | L31 => L31 | L32 => L14 | L33 => L27 | L34 => L9 end.

(* P146 : S4 S14 S19 S25 S38 S42 S53 ->
   P149 : S4 S14 S20 S31 S35 S41 S50  *)
Definition fp146_149 (p:Point) := match p with P0 => P3 | P1 => P13 | P2 => P9 | P3 => P0 | P4 => P4 | P5 => P14 | P6 => P10 | P7 => P12 | P8 => P8 | P9 => P2 | P10 => P6 | P11 => P11 | P12 => P7 | P13 => P1 | P14 => P5 end.
Definition fl146_149 (l:Line) := match l with L0 => L21 | L1 => L1 | L2 => L19 | L3 => L20 | L4 => L15 | L5 => L22 | L6 => L12 | L7 => L25 | L8 => L32 | L9 => L28 | L10 => L16 | L11 => L11 | L12 => L6 | L13 => L33 | L14 => L29 | L15 => L4 | L16 => L10 | L17 => L23 | L18 => L18 | L19 => L2 | L20 => L3 | L21 => L0 | L22 => L5 | L23 => L17 | L24 => L24 | L25 => L7 | L26 => L26 | L27 => L27 | L28 => L9 | L29 => L14 | L30 => L31 | L31 => L30 | L32 => L8 | L33 => L13 | L34 => L34 end.

(* P149 : S4 S14 S20 S31 S35 S41 S50 ->
   P150 : S5 S8 S19 S25 S37 S46 S52  *)
Definition fp149_150 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P11 | P4 => P14 | P5 => P13 | P6 => P12 | P7 => P4 | P8 => P5 | P9 => P6 | P10 => P3 | P11 => P8 | P12 => P9 | P13 => P10 | P14 => P7 end.
Definition fl149_150 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L17 | L4 => L15 | L5 => L18 | L6 => L13 | L7 => L9 | L8 => L12 | L9 => L10 | L10 => L7 | L11 => L8 | L12 => L11 | L13 => L1 | L14 => L3 | L15 => L5 | L16 => L4 | L17 => L6 | L18 => L2 | L19 => L22 | L20 => L29 | L21 => L34 | L22 => L24 | L23 => L31 | L24 => L27 | L25 => L19 | L26 => L23 | L27 => L28 | L28 => L25 | L29 => L32 | L30 => L21 | L31 => L26 | L32 => L30 | L33 => L33 | L34 => L20 end.

(* P150 : S5 S8 S19 S25 S37 S46 S52 ->
   P153 : S5 S8 S21 S28 S35 S47 S48  *)
Definition fp150_153 (p:Point) := match p with P0 => P5 | P1 => P8 | P2 => P14 | P3 => P13 | P4 => P7 | P5 => P6 | P6 => P0 | P7 => P12 | P8 => P10 | P9 => P3 | P10 => P1 | P11 => P2 | P12 => P4 | P13 => P9 | P14 => P11 end.
Definition fl150_153 (l:Line) := match l with L0 => L27 | L1 => L28 | L2 => L2 | L3 => L30 | L4 => L12 | L5 => L17 | L6 => L29 | L7 => L3 | L8 => L8 | L9 => L24 | L10 => L20 | L11 => L18 | L12 => L32 | L13 => L9 | L14 => L14 | L15 => L6 | L16 => L23 | L17 => L31 | L18 => L19 | L19 => L11 | L20 => L25 | L21 => L21 | L22 => L16 | L23 => L22 | L24 => L13 | L25 => L10 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L15 | L30 => L7 | L31 => L5 | L32 => L4 | L33 => L1 | L34 => L0 end.

(* P153 : S5 S8 S21 S28 S35 S47 S48 ->
   P155 : S5 S8 S22 S26 S39 S45 S49  *)
Definition fp153_155 (p:Point) := match p with P0 => P5 | P1 => P14 | P2 => P8 | P3 => P7 | P4 => P13 | P5 => P6 | P6 => P0 | P7 => P9 | P8 => P11 | P9 => P4 | P10 => P2 | P11 => P1 | P12 => P3 | P13 => P12 | P14 => P10 end.
Definition fl153_155 (l:Line) := match l with L0 => L27 | L1 => L28 | L2 => L2 | L3 => L29 | L4 => L17 | L5 => L12 | L6 => L30 | L7 => L6 | L8 => L14 | L9 => L19 | L10 => L23 | L11 => L9 | L12 => L31 | L13 => L18 | L14 => L8 | L15 => L3 | L16 => L20 | L17 => L32 | L18 => L24 | L19 => L13 | L20 => L22 | L21 => L26 | L22 => L10 | L23 => L25 | L24 => L11 | L25 => L16 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L7 | L30 => L15 | L31 => L4 | L32 => L5 | L33 => L1 | L34 => L0 end.

(* P155 : S5 S8 S22 S26 S39 S45 S49 ->
   P156 : S5 S9 S19 S28 S32 S45 S54  *)
Definition fp155_156 (p:Point) := match p with P0 => P7 | P1 => P4 | P2 => P12 | P3 => P14 | P4 => P6 | P5 => P9 | P6 => P1 | P7 => P11 | P8 => P3 | P9 => P8 | P10 => P0 | P11 => P2 | P12 => P10 | P13 => P5 | P14 => P13 end.
Definition fl155_156 (l:Line) := match l with L0 => L26 | L1 => L31 | L2 => L10 | L3 => L22 | L4 => L3 | L5 => L13 | L6 => L28 | L7 => L7 | L8 => L1 | L9 => L25 | L10 => L24 | L11 => L17 | L12 => L23 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L30 | L17 => L33 | L18 => L20 | L19 => L6 | L20 => L19 | L21 => L27 | L22 => L14 | L23 => L32 | L24 => L15 | L25 => L2 | L26 => L34 | L27 => L21 | L28 => L29 | L29 => L18 | L30 => L4 | L31 => L11 | L32 => L12 | L33 => L8 | L34 => L0 end.

(* P156 : S5 S9 S19 S28 S32 S45 S54 ->
   P159 : S5 S9 S20 S29 S34 S46 S49  *)
Definition fp156_159 (p:Point) := match p with P0 => P3 | P1 => P9 | P2 => P13 | P3 => P0 | P4 => P4 | P5 => P10 | P6 => P14 | P7 => P7 | P8 => P11 | P9 => P1 | P10 => P5 | P11 => P8 | P12 => P12 | P13 => P2 | P14 => P6 end.
Definition fl156_159 (l:Line) := match l with L0 => L21 | L1 => L1 | L2 => L19 | L3 => L22 | L4 => L12 | L5 => L20 | L6 => L15 | L7 => L23 | L8 => L29 | L9 => L33 | L10 => L10 | L11 => L18 | L12 => L4 | L13 => L28 | L14 => L32 | L15 => L6 | L16 => L16 | L17 => L25 | L18 => L11 | L19 => L2 | L20 => L5 | L21 => L0 | L22 => L3 | L23 => L7 | L24 => L24 | L25 => L17 | L26 => L26 | L27 => L34 | L28 => L13 | L29 => L8 | L30 => L30 | L31 => L31 | L32 => L14 | L33 => L9 | L34 => L27 end.

(* P159 : S5 S9 S20 S29 S34 S46 S49 ->
   P161 : S5 S9 S22 S30 S35 S41 S52  *)
Definition fp159_161 (p:Point) := match p with P0 => P4 | P1 => P7 | P2 => P12 | P3 => P0 | P4 => P3 | P5 => P8 | P6 => P11 | P7 => P9 | P8 => P14 | P9 => P1 | P10 => P6 | P11 => P10 | P12 => P13 | P13 => P2 | P14 => P5 end.
Definition fl159_161 (l:Line) := match l with L0 => L26 | L1 => L1 | L2 => L24 | L3 => L23 | L4 => L7 | L5 => L25 | L6 => L17 | L7 => L22 | L8 => L31 | L9 => L28 | L10 => L10 | L11 => L13 | L12 => L3 | L13 => L33 | L14 => L30 | L15 => L5 | L16 => L16 | L17 => L20 | L18 => L9 | L19 => L2 | L20 => L6 | L21 => L0 | L22 => L4 | L23 => L12 | L24 => L19 | L25 => L15 | L26 => L21 | L27 => L27 | L28 => L18 | L29 => L8 | L30 => L32 | L31 => L29 | L32 => L14 | L33 => L11 | L34 => L34 end.

(* P161 : S5 S9 S22 S30 S35 S41 S52 ->
   P162 : S5 S10 S17 S29 S32 S47 S52  *)
Definition fp161_162 (p:Point) := match p with P0 => P13 | P1 => P3 | P2 => P9 | P3 => P6 | P4 => P8 | P5 => P2 | P6 => P12 | P7 => P14 | P8 => P0 | P9 => P10 | P10 => P4 | P11 => P7 | P12 => P5 | P13 => P11 | P14 => P1 end.
Definition fl161_162 (l:Line) := match l with L0 => L21 | L1 => L32 | L2 => L16 | L3 => L6 | L4 => L25 | L5 => L28 | L6 => L11 | L7 => L20 | L8 => L1 | L9 => L12 | L10 => L19 | L11 => L22 | L12 => L15 | L13 => L23 | L14 => L10 | L15 => L33 | L16 => L29 | L17 => L18 | L18 => L4 | L19 => L7 | L20 => L2 | L21 => L34 | L22 => L31 | L23 => L8 | L24 => L3 | L25 => L24 | L26 => L27 | L27 => L0 | L28 => L14 | L29 => L13 | L30 => L17 | L31 => L9 | L32 => L5 | L33 => L30 | L34 => L26 end.

(* P162 : S5 S10 S17 S29 S32 S47 S52 ->
   P164 : S5 S10 S20 S28 S39 S41 S51  *)
Definition fp162_164 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl162_164 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P164 : S5 S10 S20 S28 S39 S41 S51 ->
   P167 : S5 S10 S21 S30 S37 S42 S49  *)
Definition fp164_167 (p:Point) := match p with P0 => P12 | P1 => P7 | P2 => P4 | P3 => P14 | P4 => P1 | P5 => P6 | P6 => P9 | P7 => P0 | P8 => P11 | P9 => P8 | P10 => P3 | P11 => P13 | P12 => P2 | P13 => P5 | P14 => P10 end.
Definition fl164_167 (l:Line) := match l with L0 => L26 | L1 => L9 | L2 => L33 | L3 => L5 | L4 => L20 | L5 => L16 | L6 => L30 | L7 => L10 | L8 => L22 | L9 => L13 | L10 => L3 | L11 => L28 | L12 => L31 | L13 => L1 | L14 => L25 | L15 => L23 | L16 => L17 | L17 => L7 | L18 => L24 | L19 => L19 | L20 => L14 | L21 => L27 | L22 => L6 | L23 => L8 | L24 => L11 | L25 => L12 | L26 => L0 | L27 => L34 | L28 => L2 | L29 => L32 | L30 => L15 | L31 => L4 | L32 => L29 | L33 => L18 | L34 => L21 end.

(* P167 : S5 S10 S21 S30 S37 S42 S49 ->
   P168 : S5 S12 S17 S26 S37 S41 S54  *)
Definition fp167_168 (p:Point) := match p with P0 => P11 | P1 => P6 | P2 => P10 | P3 => P2 | P4 => P14 | P5 => P3 | P6 => P7 | P7 => P5 | P8 => P9 | P9 => P0 | P10 => P12 | P11 => P4 | P12 => P8 | P13 => P1 | P14 => P13 end.
Definition fl167_168 (l:Line) := match l with L0 => L34 | L1 => L14 | L2 => L22 | L3 => L29 | L4 => L5 | L5 => L24 | L6 => L11 | L7 => L31 | L8 => L33 | L9 => L32 | L10 => L2 | L11 => L7 | L12 => L15 | L13 => L30 | L14 => L25 | L15 => L13 | L16 => L8 | L17 => L19 | L18 => L4 | L19 => L16 | L20 => L18 | L21 => L0 | L22 => L17 | L23 => L6 | L24 => L23 | L25 => L9 | L26 => L27 | L27 => L21 | L28 => L12 | L29 => L1 | L30 => L20 | L31 => L28 | L32 => L10 | L33 => L3 | L34 => L26 end.

(* P168 : S5 S12 S17 S26 S37 S41 S54 ->
   P171 : S5 S12 S19 S29 S39 S42 S48  *)
Definition fp168_171 (p:Point) := match p with P0 => P7 | P1 => P4 | P2 => P12 | P3 => P1 | P4 => P9 | P5 => P6 | P6 => P14 | P7 => P3 | P8 => P11 | P9 => P0 | P10 => P8 | P11 => P5 | P12 => P13 | P13 => P2 | P14 => P10 end.
Definition fl168_171 (l:Line) := match l with L0 => L26 | L1 => L10 | L2 => L31 | L3 => L22 | L4 => L3 | L5 => L28 | L6 => L13 | L7 => L23 | L8 => L24 | L9 => L25 | L10 => L1 | L11 => L17 | L12 => L7 | L13 => L20 | L14 => L30 | L15 => L9 | L16 => L16 | L17 => L33 | L18 => L5 | L19 => L8 | L20 => L11 | L21 => L0 | L22 => L12 | L23 => L4 | L24 => L29 | L25 => L18 | L26 => L21 | L27 => L34 | L28 => L15 | L29 => L2 | L30 => L32 | L31 => L19 | L32 => L14 | L33 => L6 | L34 => L27 end.

(* P171 : S5 S12 S19 S29 S39 S42 S48 ->
   P172 : S5 S12 S22 S25 S34 S47 S51  *)
Definition fp171_172 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl171_172 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P172 : S5 S12 S22 S25 S34 S47 S51 ->
   P175 : S5 S15 S17 S30 S34 S45 S48  *)
Definition fp172_175 (p:Point) := match p with P0 => P12 | P1 => P7 | P2 => P4 | P3 => P10 | P4 => P5 | P5 => P2 | P6 => P13 | P7 => P14 | P8 => P1 | P9 => P6 | P10 => P9 | P11 => P3 | P12 => P8 | P13 => P11 | P14 => P0 end.
Definition fl172_175 (l:Line) := match l with L0 => L26 | L1 => L30 | L2 => L16 | L3 => L9 | L4 => L33 | L5 => L20 | L6 => L5 | L7 => L28 | L8 => L10 | L9 => L3 | L10 => L31 | L11 => L22 | L12 => L13 | L13 => L23 | L14 => L1 | L15 => L25 | L16 => L24 | L17 => L17 | L18 => L7 | L19 => L4 | L20 => L8 | L21 => L34 | L22 => L19 | L23 => L2 | L24 => L12 | L25 => L29 | L26 => L27 | L27 => L0 | L28 => L14 | L29 => L15 | L30 => L18 | L31 => L6 | L32 => L11 | L33 => L32 | L34 => L21 end.

(* P175 : S5 S15 S17 S30 S34 S45 S48 ->
   P177 : S5 S15 S20 S25 S35 S42 S54  *)
Definition fp175_177 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl175_177 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P177 : S5 S15 S20 S25 S35 S42 S54 ->
   P178 : S5 S15 S21 S26 S32 S46 S51  *)
Definition fp177_178 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P13 | P4 => P11 | P5 => P12 | P6 => P14 | P7 => P6 | P8 => P4 | P9 => P3 | P10 => P5 | P11 => P8 | P12 => P10 | P13 => P9 | P14 => P7 end.
Definition fl177_178 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L7 | L4 => L12 | L5 => L8 | L6 => L10 | L7 => L14 | L8 => L17 | L9 => L13 | L10 => L15 | L11 => L18 | L12 => L16 | L13 => L2 | L14 => L3 | L15 => L6 | L16 => L4 | L17 => L5 | L18 => L1 | L19 => L28 | L20 => L25 | L21 => L21 | L22 => L32 | L23 => L22 | L24 => L24 | L25 => L29 | L26 => L34 | L27 => L26 | L28 => L33 | L29 => L20 | L30 => L30 | L31 => L31 | L32 => L23 | L33 => L19 | L34 => L27 end.

(* P178 : S5 S15 S21 S26 S32 S46 S51 ->
   P180 : S6 S8 S18 S25 S36 S47 S53  *)
Definition fp178_180 (p:Point) := match p with P0 => P13 | P1 => P8 | P2 => P6 | P3 => P5 | P4 => P7 | P5 => P14 | P6 => P0 | P7 => P3 | P8 => P9 | P9 => P12 | P10 => P2 | P11 => P1 | P12 => P11 | P13 => P10 | P14 => P4 end.
Definition fl178_180 (l:Line) := match l with L0 => L32 | L1 => L28 | L2 => L6 | L3 => L21 | L4 => L16 | L5 => L11 | L6 => L25 | L7 => L3 | L8 => L18 | L9 => L24 | L10 => L20 | L11 => L8 | L12 => L27 | L13 => L15 | L14 => L7 | L15 => L2 | L16 => L34 | L17 => L31 | L18 => L33 | L19 => L17 | L20 => L29 | L21 => L30 | L22 => L12 | L23 => L26 | L24 => L10 | L25 => L13 | L26 => L22 | L27 => L23 | L28 => L19 | L29 => L9 | L30 => L14 | L31 => L1 | L32 => L4 | L33 => L5 | L34 => L0 end.

(* P180 : S6 S8 S18 S25 S36 S47 S53 ->
   P182 : S6 S8 S21 S26 S37 S40 S55  *)
Definition fp180_182 (p:Point) := match p with P0 => P4 | P1 => P9 | P2 => P14 | P3 => P0 | P4 => P3 | P5 => P10 | P6 => P13 | P7 => P1 | P8 => P6 | P9 => P7 | P10 => P12 | P11 => P2 | P12 => P5 | P13 => P8 | P14 => P11 end.
Definition fl180_182 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L7 | L4 => L26 | L5 => L17 | L6 => L24 | L7 => L21 | L8 => L33 | L9 => L29 | L10 => L10 | L11 => L18 | L12 => L4 | L13 => L9 | L14 => L14 | L15 => L6 | L16 => L27 | L17 => L19 | L18 => L31 | L19 => L5 | L20 => L2 | L21 => L3 | L22 => L0 | L23 => L22 | L24 => L15 | L25 => L20 | L26 => L12 | L27 => L34 | L28 => L8 | L29 => L13 | L30 => L30 | L31 => L11 | L32 => L32 | L33 => L28 | L34 => L16 end.

(* P182 : S6 S8 S21 S26 S37 S40 S55 ->
   P185 : S6 S8 S23 S27 S39 S44 S48  *)
Definition fp182_185 (p:Point) := match p with P0 => P4 | P1 => P9 | P2 => P14 | P3 => P3 | P4 => P0 | P5 => P13 | P6 => P10 | P7 => P7 | P8 => P12 | P9 => P1 | P10 => P6 | P11 => P11 | P12 => P8 | P13 => P5 | P14 => P2 end.
Definition fl182_185 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L26 | L4 => L7 | L5 => L24 | L6 => L17 | L7 => L4 | L8 => L33 | L9 => L18 | L10 => L10 | L11 => L29 | L12 => L21 | L13 => L31 | L14 => L14 | L15 => L19 | L16 => L27 | L17 => L6 | L18 => L9 | L19 => L15 | L20 => L20 | L21 => L12 | L22 => L22 | L23 => L0 | L24 => L5 | L25 => L2 | L26 => L3 | L27 => L16 | L28 => L28 | L29 => L11 | L30 => L32 | L31 => L13 | L32 => L30 | L33 => L8 | L34 => L34 end.

(* P185 : S6 S8 S23 S27 S39 S44 S48 ->
   P186 : S6 S9 S18 S29 S32 S44 S55  *)
Definition fp185_186 (p:Point) := match p with P0 => P10 | P1 => P5 | P2 => P12 | P3 => P1 | P4 => P8 | P5 => P3 | P6 => P14 | P7 => P0 | P8 => P9 | P9 => P6 | P10 => P11 | P11 => P2 | P12 => P7 | P13 => P4 | P14 => P13 end.
Definition fl185_186 (l:Line) := match l with L0 => L30 | L1 => L8 | L2 => L19 | L3 => L4 | L4 => L34 | L5 => L13 | L6 => L25 | L7 => L27 | L8 => L29 | L9 => L28 | L10 => L2 | L11 => L17 | L12 => L12 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L26 | L17 => L20 | L18 => L33 | L19 => L11 | L20 => L10 | L21 => L7 | L22 => L0 | L23 => L32 | L24 => L18 | L25 => L24 | L26 => L3 | L27 => L21 | L28 => L1 | L29 => L15 | L30 => L22 | L31 => L6 | L32 => L23 | L33 => L31 | L34 => L14 end.

(* P186 : S6 S9 S18 S29 S32 S44 S55 ->
   P188 : S6 S9 S20 S27 S36 S41 S54  *)
Definition fp186_188 (p:Point) := match p with P0 => P5 | P1 => P12 | P2 => P10 | P3 => P9 | P4 => P11 | P5 => P6 | P6 => P0 | P7 => P4 | P8 => P2 | P9 => P7 | P10 => P13 | P11 => P14 | P12 => P8 | P13 => P1 | P14 => P3 end.
Definition fl186_188 (l:Line) := match l with L0 => L30 | L1 => L29 | L2 => L2 | L3 => L17 | L4 => L28 | L5 => L27 | L6 => L12 | L7 => L5 | L8 => L16 | L9 => L20 | L10 => L26 | L11 => L9 | L12 => L33 | L13 => L25 | L14 => L19 | L15 => L4 | L16 => L8 | L17 => L34 | L18 => L13 | L19 => L21 | L20 => L18 | L21 => L10 | L22 => L23 | L23 => L22 | L24 => L14 | L25 => L11 | L26 => L24 | L27 => L15 | L28 => L7 | L29 => L31 | L30 => L32 | L31 => L1 | L32 => L0 | L33 => L3 | L34 => L6 end.

(* P188 : S6 S9 S20 S27 S36 S41 S54 ->
   P191 : S6 S9 S23 S30 S34 S40 S53  *)
Definition fp188_191 (p:Point) := match p with P0 => P5 | P1 => P10 | P2 => P12 | P3 => P11 | P4 => P9 | P5 => P6 | P6 => P0 | P7 => P3 | P8 => P1 | P9 => P14 | P10 => P8 | P11 => P7 | P12 => P13 | P13 => P2 | P14 => P4 end.
Definition fl188_191 (l:Line) := match l with L0 => L30 | L1 => L29 | L2 => L2 | L3 => L12 | L4 => L27 | L5 => L28 | L6 => L17 | L7 => L4 | L8 => L8 | L9 => L25 | L10 => L19 | L11 => L13 | L12 => L34 | L13 => L20 | L14 => L26 | L15 => L5 | L16 => L16 | L17 => L33 | L18 => L9 | L19 => L24 | L20 => L11 | L21 => L14 | L22 => L22 | L23 => L23 | L24 => L10 | L25 => L18 | L26 => L21 | L27 => L7 | L28 => L15 | L29 => L31 | L30 => L32 | L31 => L1 | L32 => L0 | L33 => L6 | L34 => L3 end.

(* P191 : S6 S9 S23 S30 S34 S40 S53 ->
   P192 : S6 S11 S16 S25 S37 S44 S54  *)
Definition fp191_192 (p:Point) := match p with P0 => P3 | P1 => P7 | P2 => P11 | P3 => P4 | P4 => P0 | P5 => P12 | P6 => P8 | P7 => P9 | P8 => P13 | P9 => P1 | P10 => P5 | P11 => P14 | P12 => P10 | P13 => P6 | P14 => P2 end.
Definition fl191_192 (l:Line) := match l with L0 => L22 | L1 => L1 | L2 => L20 | L3 => L21 | L4 => L12 | L5 => L19 | L6 => L15 | L7 => L3 | L8 => L28 | L9 => L13 | L10 => L10 | L11 => L31 | L12 => L26 | L13 => L29 | L14 => L14 | L15 => L24 | L16 => L34 | L17 => L5 | L18 => L11 | L19 => L17 | L20 => L25 | L21 => L7 | L22 => L23 | L23 => L0 | L24 => L6 | L25 => L2 | L26 => L4 | L27 => L16 | L28 => L33 | L29 => L9 | L30 => L30 | L31 => L18 | L32 => L32 | L33 => L8 | L34 => L27 end.

(* P192 : S6 S11 S16 S25 S37 S44 S54 ->
   P195 : S6 S11 S20 S29 S39 S40 S50  *)
Definition fp192_195 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P12 | P4 => P14 | P5 => P11 | P6 => P13 | P7 => P10 | P8 => P8 | P9 => P9 | P10 => P7 | P11 => P5 | P12 => P3 | P13 => P6 | P14 => P4 end.
Definition fl192_195 (l:Line) := match l with L0 => L0 | L1 => L9 | L2 => L11 | L3 => L8 | L4 => L10 | L5 => L12 | L6 => L7 | L7 => L6 | L8 => L3 | L9 => L1 | L10 => L4 | L11 => L2 | L12 => L5 | L13 => L13 | L14 => L17 | L15 => L16 | L16 => L15 | L17 => L14 | L18 => L18 | L19 => L26 | L20 => L20 | L21 => L33 | L22 => L30 | L23 => L23 | L24 => L27 | L25 => L31 | L26 => L19 | L27 => L24 | L28 => L34 | L29 => L29 | L30 => L22 | L31 => L25 | L32 => L32 | L33 => L21 | L34 => L28 end.

(* P195 : S6 S11 S20 S29 S39 S40 S50 ->
   P196 : S6 S11 S21 S30 S36 S43 S48  *)
Definition fp195_196 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P8 | P4 => P9 | P5 => P7 | P6 => P10 | P7 => P13 | P8 => P12 | P9 => P14 | P10 => P11 | P11 => P6 | P12 => P3 | P13 => P5 | P14 => P4 end.
Definition fl195_196 (l:Line) := match l with L0 => L0 | L1 => L18 | L2 => L13 | L3 => L16 | L4 => L14 | L5 => L15 | L6 => L17 | L7 => L4 | L8 => L5 | L9 => L1 | L10 => L6 | L11 => L2 | L12 => L3 | L13 => L11 | L14 => L7 | L15 => L8 | L16 => L12 | L17 => L10 | L18 => L9 | L19 => L24 | L20 => L20 | L21 => L27 | L22 => L32 | L23 => L23 | L24 => L33 | L25 => L29 | L26 => L21 | L27 => L26 | L28 => L28 | L29 => L31 | L30 => L22 | L31 => L25 | L32 => L30 | L33 => L19 | L34 => L34 end.

(* P196 : S6 S11 S21 S30 S36 S43 S48 ->
   P199 : S6 S13 S16 S29 S34 S47 S48  *)
Definition fp196_199 (p:Point) := match p with P0 => P8 | P1 => P6 | P2 => P13 | P3 => P14 | P4 => P5 | P5 => P7 | P6 => P0 | P7 => P9 | P8 => P2 | P9 => P12 | P10 => P3 | P11 => P4 | P12 => P11 | P13 => P1 | P14 => P10 end.
Definition fl196_199 (l:Line) := match l with L0 => L32 | L1 => L27 | L2 => L3 | L3 => L18 | L4 => L20 | L5 => L24 | L6 => L8 | L7 => L2 | L8 => L15 | L9 => L34 | L10 => L33 | L11 => L7 | L12 => L31 | L13 => L21 | L14 => L25 | L15 => L6 | L16 => L11 | L17 => L28 | L18 => L16 | L19 => L19 | L20 => L14 | L21 => L9 | L22 => L23 | L23 => L30 | L24 => L17 | L25 => L12 | L26 => L29 | L27 => L13 | L28 => L10 | L29 => L26 | L30 => L22 | L31 => L4 | L32 => L0 | L33 => L5 | L34 => L1 end.

(* P199 : S6 S13 S16 S29 S34 S47 S48 ->
   P201 : S6 S13 S18 S30 S37 S41 S50  *)
Definition fp199_201 (p:Point) := match p with P0 => P9 | P1 => P4 | P2 => P14 | P3 => P7 | P4 => P1 | P5 => P12 | P6 => P6 | P7 => P3 | P8 => P13 | P9 => P0 | P10 => P10 | P11 => P11 | P12 => P5 | P13 => P8 | P14 => P2 end.
Definition fl199_201 (l:Line) := match l with L0 => L23 | L1 => L10 | L2 => L33 | L3 => L21 | L4 => L4 | L5 => L29 | L6 => L18 | L7 => L7 | L8 => L25 | L9 => L17 | L10 => L1 | L11 => L24 | L12 => L26 | L13 => L19 | L14 => L14 | L15 => L31 | L16 => L27 | L17 => L9 | L18 => L6 | L19 => L13 | L20 => L28 | L21 => L3 | L22 => L22 | L23 => L0 | L24 => L11 | L25 => L8 | L26 => L12 | L27 => L16 | L28 => L20 | L29 => L5 | L30 => L30 | L31 => L15 | L32 => L32 | L33 => L2 | L34 => L34 end.

(* P201 : S6 S13 S18 S30 S37 S41 S50 ->
   P202 : S6 S13 S23 S26 S32 S43 S54  *)
Definition fp201_202 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl201_202 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P202 : S6 S13 S23 S26 S32 S43 S54 ->
   P205 : S6 S14 S16 S26 S39 S41 S53  *)
Definition fp202_205 (p:Point) := match p with P0 => P14 | P1 => P9 | P2 => P4 | P3 => P8 | P4 => P5 | P5 => P2 | P6 => P11 | P7 => P6 | P8 => P7 | P9 => P12 | P10 => P1 | P11 => P13 | P12 => P0 | P13 => P3 | P14 => P10 end.
Definition fl202_205 (l:Line) := match l with L0 => L23 | L1 => L27 | L2 => L14 | L3 => L31 | L4 => L9 | L5 => L6 | L6 => L19 | L7 => L29 | L8 => L10 | L9 => L4 | L10 => L33 | L11 => L21 | L12 => L18 | L13 => L7 | L14 => L25 | L15 => L24 | L16 => L1 | L17 => L17 | L18 => L26 | L19 => L8 | L20 => L3 | L21 => L20 | L22 => L32 | L23 => L30 | L24 => L28 | L25 => L12 | L26 => L2 | L27 => L13 | L28 => L15 | L29 => L16 | L30 => L0 | L31 => L34 | L32 => L22 | L33 => L5 | L34 => L11 end.

(* P205 : S6 S14 S16 S26 S39 S41 S53 ->
   P206 : S6 S14 S20 S25 S34 S43 S55  *)
Definition fp205_206 (p:Point) := match p with P0 => P11 | P1 => P3 | P2 => P7 | P3 => P1 | P4 => P13 | P5 => P5 | P6 => P9 | P7 => P2 | P8 => P14 | P9 => P6 | P10 => P10 | P11 => P0 | P12 => P12 | P13 => P4 | P14 => P8 end.
Definition fl205_206 (l:Line) := match l with L0 => L22 | L1 => L11 | L2 => L29 | L3 => L14 | L4 => L34 | L5 => L5 | L6 => L24 | L7 => L21 | L8 => L19 | L9 => L20 | L10 => L15 | L11 => L1 | L12 => L12 | L13 => L13 | L14 => L3 | L15 => L10 | L16 => L26 | L17 => L28 | L18 => L31 | L19 => L8 | L20 => L9 | L21 => L7 | L22 => L0 | L23 => L32 | L24 => L6 | L25 => L25 | L26 => L16 | L27 => L27 | L28 => L17 | L29 => L2 | L30 => L30 | L31 => L18 | L32 => L23 | L33 => L33 | L34 => L4 end.

(* P206 : S6 S14 S20 S25 S34 S43 S55 ->
   P209 : S6 S14 S21 S27 S32 S47 S50  *)
Definition fp206_209 (p:Point) := match p with P0 => P7 | P1 => P3 | P2 => P11 | P3 => P2 | P4 => P10 | P5 => P6 | P6 => P14 | P7 => P1 | P8 => P9 | P9 => P5 | P10 => P13 | P11 => P0 | P12 => P8 | P13 => P4 | P14 => P12 end.
Definition fl206_209 (l:Line) := match l with L0 => L22 | L1 => L13 | L2 => L31 | L3 => L10 | L4 => L28 | L5 => L3 | L6 => L26 | L7 => L19 | L8 => L21 | L9 => L20 | L10 => L12 | L11 => L1 | L12 => L15 | L13 => L11 | L14 => L5 | L15 => L14 | L16 => L24 | L17 => L34 | L18 => L29 | L19 => L16 | L20 => L18 | L21 => L17 | L22 => L0 | L23 => L30 | L24 => L4 | L25 => L25 | L26 => L8 | L27 => L33 | L28 => L7 | L29 => L2 | L30 => L32 | L31 => L9 | L32 => L23 | L33 => L27 | L34 => L6 end.

(* P209 : S6 S14 S21 S27 S32 S47 S50 ->
   P211 : S7 S9 S18 S28 S38 S41 S53  *)
Definition fp209_211 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P4 | P4 => P3 | P5 => P5 | P6 => P6 | P7 => P10 | P8 => P9 | P9 => P7 | P10 => P8 | P11 => P13 | P12 => P14 | P13 => P12 | P14 => P11 end.
Definition fl209_211 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L15 | L8 => L18 | L9 => L14 | L10 => L13 | L11 => L16 | L12 => L17 | L13 => L8 | L14 => L11 | L15 => L7 | L16 => L9 | L17 => L12 | L18 => L10 | L19 => L24 | L20 => L23 | L21 => L26 | L22 => L25 | L23 => L22 | L24 => L21 | L25 => L20 | L26 => L19 | L27 => L29 | L28 => L30 | L29 => L28 | L30 => L27 | L31 => L34 | L32 => L33 | L33 => L31 | L34 => L32 end.

(* P211 : S7 S9 S18 S28 S38 S41 S53 ->
   P212 : S7 S9 S22 S24 S34 S45 S55  *)
Definition fp211_212 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P12 | P4 => P13 | P5 => P11 | P6 => P14 | P7 => P6 | P8 => P3 | P9 => P5 | P10 => P4 | P11 => P9 | P12 => P8 | P13 => P10 | P14 => P7 end.
Definition fl211_212 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L15 | L4 => L17 | L5 => L18 | L6 => L13 | L7 => L6 | L8 => L1 | L9 => L3 | L10 => L2 | L11 => L4 | L12 => L5 | L13 => L7 | L14 => L10 | L15 => L9 | L16 => L8 | L17 => L11 | L18 => L12 | L19 => L26 | L20 => L20 | L21 => L30 | L22 => L33 | L23 => L28 | L24 => L21 | L25 => L25 | L26 => L32 | L27 => L22 | L28 => L34 | L29 => L29 | L30 => L24 | L31 => L31 | L32 => L19 | L33 => L27 | L34 => L23 end.

(* P212 : S7 S9 S22 S24 S34 S45 S55 ->
   P215 : S7 S9 S23 S27 S32 S46 S52  *)
Definition fp212_215 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P12 | P4 => P13 | P5 => P14 | P6 => P11 | P7 => P9 | P8 => P8 | P9 => P7 | P10 => P10 | P11 => P6 | P12 => P3 | P13 => P4 | P14 => P5 end.
Definition fl212_215 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L18 | L4 => L13 | L5 => L15 | L6 => L17 | L7 => L11 | L8 => L8 | L9 => L12 | L10 => L10 | L11 => L7 | L12 => L9 | L13 => L4 | L14 => L2 | L15 => L5 | L16 => L1 | L17 => L6 | L18 => L3 | L19 => L30 | L20 => L20 | L21 => L26 | L22 => L33 | L23 => L28 | L24 => L32 | L25 => L25 | L26 => L21 | L27 => L27 | L28 => L23 | L29 => L31 | L30 => L19 | L31 => L29 | L32 => L24 | L33 => L22 | L34 => L34 end.

(* P215 : S7 S9 S23 S27 S32 S46 S52 ->
   P217 : S7 S10 S16 S31 S37 S41 S52  *)
Definition fp215_217 (p:Point) := match p with P0 => P12 | P1 => P6 | P2 => P9 | P3 => P1 | P4 => P14 | P5 => P4 | P6 => P7 | P7 => P2 | P8 => P13 | P9 => P3 | P10 => P8 | P11 => P0 | P12 => P11 | P13 => P5 | P14 => P10 end.
Definition fl215_217 (l:Line) := match l with L0 => L33 | L1 => L9 | L2 => L26 | L3 => L16 | L4 => L20 | L5 => L5 | L6 => L30 | L7 => L31 | L8 => L32 | L9 => L34 | L10 => L15 | L11 => L2 | L12 => L7 | L13 => L18 | L14 => L4 | L15 => L10 | L16 => L29 | L17 => L23 | L18 => L21 | L19 => L8 | L20 => L11 | L21 => L12 | L22 => L0 | L23 => L19 | L24 => L6 | L25 => L27 | L26 => L14 | L27 => L25 | L28 => L17 | L29 => L1 | L30 => L24 | L31 => L13 | L32 => L28 | L33 => L22 | L34 => L3 end.

(* P217 : S7 S10 S16 S31 S37 S41 S52 ->
   P219 : S7 S10 S21 S28 S32 S43 S55  *)
Definition fp217_219 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl217_219 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P219 : S7 S10 S21 S28 S32 S43 S55 ->
   P220 : S7 S10 S23 S24 S39 S42 S53  *)
Definition fp219_220 (p:Point) := match p with P0 => P10 | P1 => P13 | P2 => P4 | P3 => P7 | P4 => P2 | P5 => P5 | P6 => P12 | P7 => P3 | P8 => P14 | P9 => P9 | P10 => P0 | P11 => P11 | P12 => P6 | P13 => P1 | P14 => P8 end.
Definition fl219_220 (l:Line) := match l with L0 => L25 | L1 => L13 | L2 => L30 | L3 => L19 | L4 => L4 | L5 => L34 | L6 => L8 | L7 => L16 | L8 => L6 | L9 => L32 | L10 => L21 | L11 => L11 | L12 => L28 | L13 => L1 | L14 => L24 | L15 => L26 | L16 => L7 | L17 => L17 | L18 => L23 | L19 => L3 | L20 => L31 | L21 => L10 | L22 => L22 | L23 => L18 | L24 => L14 | L25 => L0 | L26 => L15 | L27 => L27 | L28 => L12 | L29 => L29 | L30 => L2 | L31 => L20 | L32 => L9 | L33 => L33 | L34 => L5 end.

(* P220 : S7 S10 S23 S24 S39 S42 S53 ->
   P223 : S7 S11 S16 S28 S39 S45 S48  *)
Definition fp220_223 (p:Point) := match p with P0 => P9 | P1 => P6 | P2 => P12 | P3 => P8 | P4 => P2 | P5 => P13 | P6 => P3 | P7 => P14 | P8 => P4 | P9 => P7 | P10 => P1 | P11 => P5 | P12 => P11 | P13 => P0 | P14 => P10 end.
Definition fl220_223 (l:Line) := match l with L0 => L33 | L1 => L18 | L2 => L21 | L3 => L23 | L4 => L10 | L5 => L29 | L6 => L4 | L7 => L15 | L8 => L7 | L9 => L34 | L10 => L31 | L11 => L2 | L12 => L32 | L13 => L9 | L14 => L30 | L15 => L20 | L16 => L5 | L17 => L16 | L18 => L26 | L19 => L8 | L20 => L24 | L21 => L3 | L22 => L27 | L23 => L13 | L24 => L17 | L25 => L0 | L26 => L14 | L27 => L25 | L28 => L6 | L29 => L28 | L30 => L11 | L31 => L19 | L32 => L1 | L33 => L22 | L34 => L12 end.

(* P223 : S7 S11 S16 S28 S39 S45 S48 ->
   P224 : S7 S11 S21 S24 S37 S46 S50  *)
Definition fp223_224 (p:Point) := match p with P0 => P6 | P1 => P9 | P2 => P12 | P3 => P10 | P4 => P11 | P5 => P0 | P6 => P5 | P7 => P4 | P8 => P1 | P9 => P14 | P10 => P7 | P11 => P13 | P12 => P8 | P13 => P3 | P14 => P2 end.
Definition fl223_224 (l:Line) := match l with L0 => L33 | L1 => L34 | L2 => L2 | L3 => L7 | L4 => L31 | L5 => L32 | L6 => L15 | L7 => L29 | L8 => L10 | L9 => L18 | L10 => L23 | L11 => L21 | L12 => L4 | L13 => L26 | L14 => L16 | L15 => L30 | L16 => L20 | L17 => L5 | L18 => L9 | L19 => L13 | L20 => L8 | L21 => L19 | L22 => L25 | L23 => L14 | L24 => L11 | L25 => L22 | L26 => L24 | L27 => L0 | L28 => L1 | L29 => L6 | L30 => L3 | L31 => L17 | L32 => L12 | L33 => L27 | L34 => L28 end.

(* P224 : S7 S11 S21 S24 S37 S46 S50 ->
   P227 : S7 S11 S22 S25 S38 S43 S52  *)
Definition fp224_227 (p:Point) := match p with P0 => P6 | P1 => P9 | P2 => P12 | P3 => P10 | P4 => P11 | P5 => P0 | P6 => P5 | P7 => P4 | P8 => P1 | P9 => P14 | P10 => P7 | P11 => P13 | P12 => P8 | P13 => P3 | P14 => P2 end.
Definition fl224_227 (l:Line) := match l with L0 => L33 | L1 => L34 | L2 => L2 | L3 => L7 | L4 => L31 | L5 => L32 | L6 => L15 | L7 => L29 | L8 => L10 | L9 => L18 | L10 => L23 | L11 => L21 | L12 => L4 | L13 => L26 | L14 => L16 | L15 => L30 | L16 => L20 | L17 => L5 | L18 => L9 | L19 => L13 | L20 => L8 | L21 => L19 | L22 => L25 | L23 => L14 | L24 => L11 | L25 => L22 | L26 => L24 | L27 => L0 | L28 => L1 | L29 => L6 | L30 => L3 | L31 => L17 | L32 => L12 | L33 => L27 | L34 => L28 end.

(* P227 : S7 S11 S22 S25 S38 S43 S52 ->
   P228 : S7 S12 S18 S25 S37 S42 S55  *)
Definition fp227_228 (p:Point) := match p with P0 => P9 | P1 => P12 | P2 => P6 | P3 => P7 | P4 => P1 | P5 => P4 | P6 => P14 | P7 => P3 | P8 => P13 | P9 => P8 | P10 => P2 | P11 => P11 | P12 => P5 | P13 => P0 | P14 => P10 end.
Definition fl227_228 (l:Line) := match l with L0 => L33 | L1 => L10 | L2 => L23 | L3 => L21 | L4 => L18 | L5 => L29 | L6 => L4 | L7 => L9 | L8 => L16 | L9 => L30 | L10 => L20 | L11 => L5 | L12 => L26 | L13 => L15 | L14 => L34 | L15 => L31 | L16 => L2 | L17 => L7 | L18 => L32 | L19 => L13 | L20 => L28 | L21 => L3 | L22 => L22 | L23 => L8 | L24 => L11 | L25 => L0 | L26 => L12 | L27 => L25 | L28 => L1 | L29 => L24 | L30 => L17 | L31 => L19 | L32 => L6 | L33 => L27 | L34 => L14 end.

(* P228 : S7 S12 S18 S25 S37 S42 S55 ->
   P231 : S7 S12 S22 S27 S39 S41 S50  *)
Definition fp228_231 (p:Point) := match p with P0 => P11 | P1 => P3 | P2 => P7 | P3 => P2 | P4 => P14 | P5 => P6 | P6 => P10 | P7 => P0 | P8 => P12 | P9 => P4 | P10 => P8 | P11 => P1 | P12 => P13 | P13 => P5 | P14 => P9 end.
Definition fl228_231 (l:Line) := match l with L0 => L22 | L1 => L14 | L2 => L34 | L3 => L5 | L4 => L24 | L5 => L11 | L6 => L29 | L7 => L19 | L8 => L20 | L9 => L21 | L10 => L1 | L11 => L12 | L12 => L15 | L13 => L3 | L14 => L10 | L15 => L13 | L16 => L28 | L17 => L31 | L18 => L26 | L19 => L18 | L20 => L16 | L21 => L17 | L22 => L0 | L23 => L23 | L24 => L9 | L25 => L27 | L26 => L6 | L27 => L33 | L28 => L2 | L29 => L7 | L30 => L32 | L31 => L4 | L32 => L30 | L33 => L25 | L34 => L8 end.

(* P231 : S7 S12 S22 S27 S39 S41 S50 ->
   P233 : S7 S12 S23 S31 S34 S43 S48  *)
Definition fp231_233 (p:Point) := match p with P0 => P11 | P1 => P7 | P2 => P3 | P3 => P2 | P4 => P14 | P5 => P10 | P6 => P6 | P7 => P1 | P8 => P13 | P9 => P9 | P10 => P5 | P11 => P0 | P12 => P12 | P13 => P8 | P14 => P4 end.
Definition fl231_233 (l:Line) := match l with L0 => L22 | L1 => L14 | L2 => L34 | L3 => L11 | L4 => L29 | L5 => L5 | L6 => L24 | L7 => L31 | L8 => L28 | L9 => L26 | L10 => L10 | L11 => L3 | L12 => L13 | L13 => L12 | L14 => L1 | L15 => L15 | L16 => L20 | L17 => L19 | L18 => L21 | L19 => L17 | L20 => L16 | L21 => L18 | L22 => L0 | L23 => L23 | L24 => L6 | L25 => L27 | L26 => L9 | L27 => L25 | L28 => L8 | L29 => L4 | L30 => L30 | L31 => L7 | L32 => L32 | L33 => L33 | L34 => L2 end.

(* P233 : S7 S12 S23 S31 S34 S43 S48 ->
   P234 : S7 S15 S16 S25 S34 S46 S53  *)
Definition fp233_234 (p:Point) := match p with P0 => P9 | P1 => P6 | P2 => P12 | P3 => P8 | P4 => P2 | P5 => P13 | P6 => P3 | P7 => P14 | P8 => P4 | P9 => P7 | P10 => P1 | P11 => P5 | P12 => P11 | P13 => P0 | P14 => P10 end.
Definition fl233_234 (l:Line) := match l with L0 => L33 | L1 => L18 | L2 => L21 | L3 => L23 | L4 => L10 | L5 => L29 | L6 => L4 | L7 => L15 | L8 => L7 | L9 => L34 | L10 => L31 | L11 => L2 | L12 => L32 | L13 => L9 | L14 => L30 | L15 => L20 | L16 => L5 | L17 => L16 | L18 => L26 | L19 => L8 | L20 => L24 | L21 => L3 | L22 => L27 | L23 => L13 | L24 => L17 | L25 => L0 | L26 => L14 | L27 => L25 | L28 => L6 | L29 => L28 | L30 => L11 | L31 => L19 | L32 => L1 | L33 => L22 | L34 => L12 end.

(* P234 : S7 S15 S16 S25 S34 S46 S53 ->
   P237 : S7 S15 S18 S31 S32 S45 S50  *)
Definition fp234_237 (p:Point) := match p with P0 => P4 | P1 => P13 | P2 => P10 | P3 => P3 | P4 => P0 | P5 => P9 | P6 => P14 | P7 => P7 | P8 => P12 | P9 => P5 | P10 => P2 | P11 => P11 | P12 => P8 | P13 => P1 | P14 => P6 end.
Definition fl234_237 (l:Line) := match l with L0 => L25 | L1 => L1 | L2 => L23 | L3 => L26 | L4 => L17 | L5 => L24 | L6 => L7 | L7 => L6 | L8 => L16 | L9 => L32 | L10 => L28 | L11 => L11 | L12 => L21 | L13 => L13 | L14 => L34 | L15 => L19 | L16 => L8 | L17 => L4 | L18 => L30 | L19 => L15 | L20 => L20 | L21 => L12 | L22 => L22 | L23 => L2 | L24 => L5 | L25 => L0 | L26 => L3 | L27 => L33 | L28 => L10 | L29 => L29 | L30 => L18 | L31 => L31 | L32 => L9 | L33 => L27 | L34 => L14 end.

(* P237 : S7 S15 S18 S31 S32 S45 S50 ->
   P239 : S7 S15 S21 S27 S38 S42 S48  *)
Definition fp237_239 (p:Point) := match p with P0 => P3 | P1 => P11 | P2 => P7 | P3 => P4 | P4 => P0 | P5 => P8 | P6 => P12 | P7 => P10 | P8 => P14 | P9 => P6 | P10 => P2 | P11 => P13 | P12 => P9 | P13 => P1 | P14 => P5 end.
Definition fl237_239 (l:Line) := match l with L0 => L22 | L1 => L1 | L2 => L20 | L3 => L19 | L4 => L15 | L5 => L21 | L6 => L12 | L7 => L5 | L8 => L14 | L9 => L29 | L10 => L34 | L11 => L11 | L12 => L24 | L13 => L13 | L14 => L28 | L15 => L26 | L16 => L10 | L17 => L3 | L18 => L31 | L19 => L17 | L20 => L23 | L21 => L7 | L22 => L25 | L23 => L2 | L24 => L6 | L25 => L0 | L26 => L4 | L27 => L27 | L28 => L8 | L29 => L32 | L30 => L18 | L31 => L30 | L32 => L9 | L33 => L33 | L34 => L16 end.

(* P239 : S7 S15 S21 S27 S38 S42 S48 ->
   P0 : S0 S9 S19 S24 S36 S46 S53  *)
Definition fp239_0 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P3 | P4 => P4 | P5 => P5 | P6 => P6 | P7 => P14 | P8 => P13 | P9 => P12 | P10 => P11 | P11 => P10 | P12 => P9 | P13 => P8 | P14 => P7 end.
Definition fl239_0 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L6 | L4 => L5 | L5 => L4 | L6 => L3 | L7 => L7 | L8 => L11 | L9 => L10 | L10 => L9 | L11 => L8 | L12 => L12 | L13 => L14 | L14 => L13 | L15 => L15 | L16 => L18 | L17 => L17 | L18 => L16 | L19 => L22 | L20 => L21 | L21 => L20 | L22 => L19 | L23 => L26 | L24 => L25 | L25 => L24 | L26 => L23 | L27 => L28 | L28 => L27 | L29 => L30 | L30 => L29 | L31 => L31 | L32 => L32 | L33 => L33 | L34 => L34 end.

(* ~~~~~~~~~~ CLASS 1 ~~~~~~~~~~ *)
(* P1 : S0 S9 S19 S28 S38 S40 S53 ->
   P2 : S0 S9 S20 S27 S36 S46 S49  *)
Definition fp1_2 (p:Point) := match p with P0 => P3 | P1 => P10 | P2 => P14 | P3 => P4 | P4 => P0 | P5 => P13 | P6 => P9 | P7 => P5 | P8 => P1 | P9 => P12 | P10 => P8 | P11 => P2 | P12 => P6 | P13 => P7 | P14 => P11 end.
Definition fl1_2 (l:Line) := match l with L0 => L19 | L1 => L1 | L2 => L21 | L3 => L12 | L4 => L20 | L5 => L15 | L6 => L22 | L7 => L4 | L8 => L8 | L9 => L34 | L10 => L30 | L11 => L13 | L12 => L25 | L13 => L27 | L14 => L14 | L15 => L23 | L16 => L31 | L17 => L6 | L18 => L9 | L19 => L24 | L20 => L7 | L21 => L26 | L22 => L17 | L23 => L5 | L24 => L0 | L25 => L3 | L26 => L2 | L27 => L11 | L28 => L28 | L29 => L16 | L30 => L32 | L31 => L29 | L32 => L10 | L33 => L33 | L34 => L18 end.

(* P2 : S0 S9 S20 S27 S36 S46 S49 ->
   P4 : S0 S9 S22 S24 S35 S44 S55  *)
Definition fp2_4 (p:Point) := match p with P0 => P3 | P1 => P10 | P2 => P14 | P3 => P0 | P4 => P4 | P5 => P9 | P6 => P13 | P7 => P12 | P8 => P8 | P9 => P5 | P10 => P1 | P11 => P11 | P12 => P7 | P13 => P6 | P14 => P2 end.
Definition fl2_4 (l:Line) := match l with L0 => L19 | L1 => L1 | L2 => L21 | L3 => L20 | L4 => L12 | L5 => L22 | L6 => L15 | L7 => L25 | L8 => L8 | L9 => L13 | L10 => L30 | L11 => L34 | L12 => L4 | L13 => L9 | L14 => L14 | L15 => L6 | L16 => L31 | L17 => L23 | L18 => L27 | L19 => L0 | L20 => L3 | L21 => L2 | L22 => L5 | L23 => L17 | L24 => L24 | L25 => L7 | L26 => L26 | L27 => L18 | L28 => L33 | L29 => L29 | L30 => L10 | L31 => L16 | L32 => L32 | L33 => L28 | L34 => L11 end.

(* P4 : S0 S9 S22 S24 S35 S44 S55 ->
   P7 : S0 S10 S16 S31 S37 S44 S49  *)
Definition fp4_7 (p:Point) := match p with P0 => P5 | P1 => P13 | P2 => P7 | P3 => P11 | P4 => P9 | P5 => P1 | P6 => P3 | P7 => P0 | P8 => P6 | P9 => P14 | P10 => P8 | P11 => P12 | P12 => P10 | P13 => P2 | P14 => P4 end.
Definition fl4_7 (l:Line) := match l with L0 => L28 | L1 => L29 | L2 => L12 | L3 => L2 | L4 => L27 | L5 => L30 | L6 => L17 | L7 => L21 | L8 => L32 | L9 => L25 | L10 => L6 | L11 => L16 | L12 => L11 | L13 => L3 | L14 => L26 | L15 => L22 | L16 => L13 | L17 => L10 | L18 => L31 | L19 => L24 | L20 => L34 | L21 => L14 | L22 => L5 | L23 => L23 | L24 => L33 | L25 => L18 | L26 => L4 | L27 => L7 | L28 => L0 | L29 => L9 | L30 => L8 | L31 => L1 | L32 => L15 | L33 => L19 | L34 => L20 end.

(* P7 : S0 S10 S16 S31 S37 S44 S49 ->
   P8 : S0 S10 S17 S24 S36 S47 S53  *)
Definition fp7_8 (p:Point) := match p with P0 => P14 | P1 => P10 | P2 => P3 | P3 => P1 | P4 => P12 | P5 => P8 | P6 => P5 | P7 => P4 | P8 => P9 | P9 => P13 | P10 => P0 | P11 => P6 | P12 => P7 | P13 => P11 | P14 => P2 end.
Definition fl7_8 (l:Line) := match l with L0 => L19 | L1 => L9 | L2 => L27 | L3 => L23 | L4 => L6 | L5 => L31 | L6 => L14 | L7 => L30 | L8 => L4 | L9 => L13 | L10 => L25 | L11 => L34 | L12 => L8 | L13 => L1 | L14 => L15 | L15 => L12 | L16 => L22 | L17 => L20 | L18 => L21 | L19 => L0 | L20 => L10 | L21 => L11 | L22 => L7 | L23 => L16 | L24 => L33 | L25 => L5 | L26 => L26 | L27 => L18 | L28 => L24 | L29 => L32 | L30 => L3 | L31 => L17 | L32 => L29 | L33 => L28 | L34 => L2 end.

(* P8 : S0 S10 S17 S24 S36 S47 S53 ->
   P10 : S0 S10 S20 S28 S33 S43 S55  *)
Definition fp8_10 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl8_10 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P10 : S0 S10 S20 S28 S33 S43 S55 ->
   P12 : S0 S12 S17 S26 S37 S40 S55  *)
Definition fp10_12 (p:Point) := match p with P0 => P6 | P1 => P12 | P2 => P9 | P3 => P13 | P4 => P8 | P5 => P2 | P6 => P3 | P7 => P1 | P8 => P4 | P9 => P14 | P10 => P7 | P11 => P11 | P12 => P10 | P13 => P0 | P14 => P5 end.
Definition fl10_12 (l:Line) := match l with L0 => L33 | L1 => L32 | L2 => L15 | L3 => L7 | L4 => L31 | L5 => L34 | L6 => L2 | L7 => L20 | L8 => L26 | L9 => L30 | L10 => L9 | L11 => L5 | L12 => L16 | L13 => L10 | L14 => L29 | L15 => L21 | L16 => L4 | L17 => L18 | L18 => L23 | L19 => L28 | L20 => L25 | L21 => L6 | L22 => L11 | L23 => L27 | L24 => L24 | L25 => L3 | L26 => L8 | L27 => L17 | L28 => L0 | L29 => L14 | L30 => L13 | L31 => L12 | L32 => L1 | L33 => L19 | L34 => L22 end.

(* P12 : S0 S12 S17 S26 S37 S40 S55 ->
   P14 : S0 S12 S19 S31 S36 S43 S48  *)
Definition fp12_14 (p:Point) := match p with P0 => P14 | P1 => P10 | P2 => P3 | P3 => P11 | P4 => P2 | P5 => P6 | P6 => P7 | P7 => P12 | P8 => P1 | P9 => P5 | P10 => P8 | P11 => P0 | P12 => P13 | P13 => P9 | P14 => P4 end.
Definition fl12_14 (l:Line) := match l with L0 => L19 | L1 => L14 | L2 => L31 | L3 => L9 | L4 => L27 | L5 => L6 | L6 => L23 | L7 => L13 | L8 => L8 | L9 => L25 | L10 => L30 | L11 => L4 | L12 => L34 | L13 => L20 | L14 => L1 | L15 => L22 | L16 => L21 | L17 => L15 | L18 => L12 | L19 => L24 | L20 => L11 | L21 => L29 | L22 => L5 | L23 => L17 | L24 => L0 | L25 => L18 | L26 => L16 | L27 => L7 | L28 => L33 | L29 => L2 | L30 => L32 | L31 => L26 | L32 => L10 | L33 => L28 | L34 => L3 end.

(* P14 : S0 S12 S19 S31 S36 S43 S48 ->
   P17 : S0 S12 S22 S27 S33 S47 S50  *)
Definition fp14_17 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl14_17 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P17 : S0 S12 S22 S27 S33 S47 S50 ->
   P19 : S0 S13 S16 S28 S35 S47 S48  *)
Definition fp17_19 (p:Point) := match p with P0 => P9 | P1 => P6 | P2 => P12 | P3 => P7 | P4 => P1 | P5 => P14 | P6 => P4 | P7 => P10 | P8 => P0 | P9 => P11 | P10 => P5 | P11 => P2 | P12 => P8 | P13 => P3 | P14 => P13 end.
Definition fl17_19 (l:Line) := match l with L0 => L33 | L1 => L10 | L2 => L23 | L3 => L4 | L4 => L29 | L5 => L18 | L6 => L21 | L7 => L7 | L8 => L2 | L9 => L32 | L10 => L34 | L11 => L15 | L12 => L31 | L13 => L30 | L14 => L16 | L15 => L26 | L16 => L20 | L17 => L9 | L18 => L5 | L19 => L28 | L20 => L3 | L21 => L22 | L22 => L13 | L23 => L11 | L24 => L0 | L25 => L12 | L26 => L8 | L27 => L6 | L28 => L19 | L29 => L14 | L30 => L27 | L31 => L25 | L32 => L1 | L33 => L24 | L34 => L17 end.

(* P19 : S0 S13 S16 S28 S35 S47 S48 ->
   P20 : S0 S13 S19 S24 S37 S46 S50  *)
Definition fp19_20 (p:Point) := match p with P0 => P5 | P1 => P13 | P2 => P7 | P3 => P8 | P4 => P14 | P5 => P6 | P6 => P0 | P7 => P12 | P8 => P10 | P9 => P2 | P10 => P4 | P11 => P3 | P12 => P1 | P13 => P9 | P14 => P11 end.
Definition fl19_20 (l:Line) := match l with L0 => L28 | L1 => L27 | L2 => L2 | L3 => L30 | L4 => L17 | L5 => L12 | L6 => L29 | L7 => L6 | L8 => L25 | L9 => L11 | L10 => L16 | L11 => L21 | L12 => L32 | L13 => L26 | L14 => L22 | L15 => L3 | L16 => L10 | L17 => L31 | L18 => L13 | L19 => L24 | L20 => L8 | L21 => L18 | L22 => L20 | L23 => L14 | L24 => L19 | L25 => L23 | L26 => L9 | L27 => L34 | L28 => L33 | L29 => L15 | L30 => L7 | L31 => L5 | L32 => L4 | L33 => L0 | L34 => L1 end.

(* P20 : S0 S13 S19 S24 S37 S46 S50 ->
   P23 : S0 S13 S22 S26 S38 S43 S49  *)
Definition fp20_23 (p:Point) := match p with P0 => P5 | P1 => P7 | P2 => P13 | P3 => P14 | P4 => P8 | P5 => P6 | P6 => P0 | P7 => P9 | P8 => P11 | P9 => P1 | P10 => P3 | P11 => P4 | P12 => P2 | P13 => P12 | P14 => P10 end.
Definition fl20_23 (l:Line) := match l with L0 => L28 | L1 => L27 | L2 => L2 | L3 => L29 | L4 => L12 | L5 => L17 | L6 => L30 | L7 => L3 | L8 => L22 | L9 => L13 | L10 => L10 | L11 => L26 | L12 => L31 | L13 => L21 | L14 => L25 | L15 => L6 | L16 => L16 | L17 => L32 | L18 => L11 | L19 => L19 | L20 => L14 | L21 => L9 | L22 => L23 | L23 => L8 | L24 => L24 | L25 => L20 | L26 => L18 | L27 => L34 | L28 => L33 | L29 => L7 | L30 => L15 | L31 => L4 | L32 => L5 | L33 => L0 | L34 => L1 end.

(* P23 : S0 S13 S22 S26 S38 S43 S49 ->
   P24 : S0 S15 S16 S26 S33 S46 S53  *)
Definition fp23_24 (p:Point) := match p with P0 => P9 | P1 => P12 | P2 => P6 | P3 => P2 | P4 => P8 | P5 => P13 | P6 => P3 | P7 => P5 | P8 => P11 | P9 => P10 | P10 => P0 | P11 => P4 | P12 => P14 | P13 => P7 | P14 => P1 end.
Definition fl23_24 (l:Line) := match l with L0 => L33 | L1 => L18 | L2 => L21 | L3 => L29 | L4 => L4 | L5 => L23 | L6 => L10 | L7 => L20 | L8 => L5 | L9 => L9 | L10 => L30 | L11 => L26 | L12 => L16 | L13 => L2 | L14 => L7 | L15 => L15 | L16 => L31 | L17 => L32 | L18 => L34 | L19 => L0 | L20 => L14 | L21 => L13 | L22 => L17 | L23 => L8 | L24 => L24 | L25 => L3 | L26 => L27 | L27 => L11 | L28 => L28 | L29 => L25 | L30 => L6 | L31 => L12 | L32 => L22 | L33 => L19 | L34 => L1 end.

(* P24 : S0 S15 S16 S26 S33 S46 S53 ->
   P27 : S0 S15 S17 S27 S38 S44 S48  *)
Definition fp24_27 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P13 | P4 => P11 | P5 => P14 | P6 => P12 | P7 => P10 | P8 => P8 | P9 => P9 | P10 => P7 | P11 => P4 | P12 => P6 | P13 => P3 | P14 => P5 end.
Definition fl24_27 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L8 | L4 => L10 | L5 => L7 | L6 => L12 | L7 => L5 | L8 => L3 | L9 => L2 | L10 => L4 | L11 => L1 | L12 => L6 | L13 => L13 | L14 => L17 | L15 => L16 | L16 => L15 | L17 => L14 | L18 => L18 | L19 => L28 | L20 => L32 | L21 => L21 | L22 => L25 | L23 => L29 | L24 => L24 | L25 => L22 | L26 => L34 | L27 => L27 | L28 => L19 | L29 => L23 | L30 => L31 | L31 => L30 | L32 => L20 | L33 => L33 | L34 => L26 end.

(* P27 : S0 S15 S17 S27 S38 S44 S48 ->
   P29 : S0 S15 S20 S31 S35 S40 S50  *)
Definition fp27_29 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl27_29 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P29 : S0 S15 S20 S31 S35 S40 S50 ->
   P30 : S1 S8 S18 S28 S33 S47 S53  *)
Definition fp29_30 (p:Point) := match p with P0 => P10 | P1 => P14 | P2 => P3 | P3 => P8 | P4 => P1 | P5 => P5 | P6 => P12 | P7 => P9 | P8 => P0 | P9 => P4 | P10 => P13 | P11 => P2 | P12 => P7 | P13 => P11 | P14 => P6 end.
Definition fl29_30 (l:Line) := match l with L0 => L19 | L1 => L8 | L2 => L30 | L3 => L4 | L4 => L25 | L5 => L13 | L6 => L34 | L7 => L9 | L8 => L6 | L9 => L31 | L10 => L23 | L11 => L14 | L12 => L27 | L13 => L21 | L14 => L15 | L15 => L20 | L16 => L22 | L17 => L12 | L18 => L1 | L19 => L32 | L20 => L3 | L21 => L24 | L22 => L18 | L23 => L7 | L24 => L0 | L25 => L11 | L26 => L10 | L27 => L2 | L28 => L29 | L29 => L17 | L30 => L28 | L31 => L33 | L32 => L5 | L33 => L26 | L34 => L16 end.

(* P30 : S1 S8 S18 S28 S33 S47 S53 ->
   P33 : S1 S8 S19 S31 S37 S40 S52  *)
Definition fp30_33 (p:Point) := match p with P0 => P10 | P1 => P3 | P2 => P14 | P3 => P1 | P4 => P8 | P5 => P5 | P6 => P12 | P7 => P13 | P8 => P4 | P9 => P9 | P10 => P0 | P11 => P11 | P12 => P6 | P13 => P7 | P14 => P2 end.
Definition fl30_33 (l:Line) := match l with L0 => L19 | L1 => L8 | L2 => L30 | L3 => L25 | L4 => L4 | L5 => L34 | L6 => L13 | L7 => L20 | L8 => L1 | L9 => L15 | L10 => L21 | L11 => L22 | L12 => L12 | L13 => L6 | L14 => L14 | L15 => L9 | L16 => L31 | L17 => L27 | L18 => L23 | L19 => L0 | L20 => L7 | L21 => L10 | L22 => L11 | L23 => L18 | L24 => L24 | L25 => L3 | L26 => L32 | L27 => L17 | L28 => L28 | L29 => L29 | L30 => L2 | L31 => L16 | L32 => L26 | L33 => L33 | L34 => L5 end.

(* P33 : S1 S8 S19 S31 S37 S40 S52 ->
   P35 : S1 S8 S22 S27 S39 S44 S49  *)
Definition fp33_35 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl33_35 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P35 : S1 S8 S22 S27 S39 S44 S49 ->
   P36 : S1 S11 S17 S24 S37 S44 S54  *)
Definition fp35_36 (p:Point) := match p with P0 => P9 | P1 => P11 | P2 => P5 | P3 => P8 | P4 => P2 | P5 => P4 | P6 => P14 | P7 => P0 | P8 => P10 | P9 => P12 | P10 => P6 | P11 => P7 | P12 => P1 | P13 => P3 | P14 => P13 end.
Definition fl35_36 (l:Line) := match l with L0 => L29 | L1 => L18 | L2 => L23 | L3 => L4 | L4 => L33 | L5 => L10 | L6 => L21 | L7 => L14 | L8 => L34 | L9 => L11 | L10 => L5 | L11 => L22 | L12 => L24 | L13 => L2 | L14 => L28 | L15 => L27 | L16 => L12 | L17 => L17 | L18 => L30 | L19 => L32 | L20 => L8 | L21 => L20 | L22 => L3 | L23 => L16 | L24 => L13 | L25 => L15 | L26 => L0 | L27 => L25 | L28 => L1 | L29 => L26 | L30 => L7 | L31 => L6 | L32 => L19 | L33 => L9 | L34 => L31 end.

(* P36 : S1 S11 S17 S24 S37 S44 S54 ->
   P39 : S1 S11 S20 S28 S39 S40 S51  *)
Definition fp36_39 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl36_39 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P39 : S1 S11 S20 S28 S39 S40 S51 ->
   P41 : S1 S11 S22 S30 S33 S43 S52  *)
Definition fp39_41 (p:Point) := match p with P0 => P12 | P1 => P4 | P2 => P7 | P3 => P1 | P4 => P14 | P5 => P6 | P6 => P9 | P7 => P10 | P8 => P5 | P9 => P13 | P10 => P2 | P11 => P8 | P12 => P3 | P13 => P11 | P14 => P0 end.
Definition fl39_41 (l:Line) := match l with L0 => L26 | L1 => L9 | L2 => L33 | L3 => L30 | L4 => L16 | L5 => L20 | L6 => L5 | L7 => L23 | L8 => L17 | L9 => L1 | L10 => L25 | L11 => L24 | L12 => L7 | L13 => L13 | L14 => L3 | L15 => L10 | L16 => L22 | L17 => L31 | L18 => L28 | L19 => L0 | L20 => L12 | L21 => L11 | L22 => L8 | L23 => L6 | L24 => L27 | L25 => L14 | L26 => L19 | L27 => L2 | L28 => L34 | L29 => L32 | L30 => L15 | L31 => L4 | L32 => L29 | L33 => L21 | L34 => L18 end.

(* P41 : S1 S11 S22 S30 S33 S43 S52 ->
   P43 : S1 S13 S18 S30 S37 S42 S49  *)
Definition fp41_43 (p:Point) := match p with P0 => P10 | P1 => P14 | P2 => P3 | P3 => P11 | P4 => P6 | P5 => P2 | P6 => P7 | P7 => P13 | P8 => P4 | P9 => P0 | P10 => P9 | P11 => P1 | P12 => P8 | P13 => P12 | P14 => P5 end.
Definition fl41_43 (l:Line) := match l with L0 => L19 | L1 => L34 | L2 => L13 | L3 => L25 | L4 => L4 | L5 => L8 | L6 => L30 | L7 => L31 | L8 => L23 | L9 => L27 | L10 => L6 | L11 => L9 | L12 => L14 | L13 => L21 | L14 => L12 | L15 => L22 | L16 => L20 | L17 => L15 | L18 => L1 | L19 => L29 | L20 => L24 | L21 => L5 | L22 => L11 | L23 => L2 | L24 => L7 | L25 => L33 | L26 => L32 | L27 => L17 | L28 => L16 | L29 => L0 | L30 => L18 | L31 => L28 | L32 => L26 | L33 => L3 | L34 => L10 end.

(* P43 : S1 S13 S18 S30 S37 S42 S49 ->
   P45 : S1 S13 S19 S28 S32 S43 S54  *)
Definition fp43_45 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P9 | P4 => P7 | P5 => P8 | P6 => P10 | P7 => P12 | P8 => P14 | P9 => P13 | P10 => P11 | P11 => P6 | P12 => P4 | P13 => P3 | P14 => P5 end.
Definition fl43_45 (l:Line) := match l with L0 => L0 | L1 => L10 | L2 => L8 | L3 => L9 | L4 => L11 | L5 => L7 | L6 => L12 | L7 => L13 | L8 => L14 | L9 => L17 | L10 => L16 | L11 => L15 | L12 => L18 | L13 => L5 | L14 => L2 | L15 => L4 | L16 => L1 | L17 => L3 | L18 => L6 | L19 => L29 | L20 => L23 | L21 => L21 | L22 => L33 | L23 => L28 | L24 => L31 | L25 => L22 | L26 => L26 | L27 => L27 | L28 => L20 | L29 => L32 | L30 => L24 | L31 => L30 | L32 => L19 | L33 => L25 | L34 => L34 end.

(* P45 : S1 S13 S19 S28 S32 S43 S54 ->
   P46 : S1 S13 S22 S24 S34 S47 S51  *)
Definition fp45_46 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl45_46 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P46 : S1 S13 S22 S24 S34 S47 S51 ->
   P49 : S1 S14 S17 S27 S32 S47 S52  *)
Definition fp46_49 (p:Point) := match p with P0 => P11 | P1 => P9 | P2 => P5 | P3 => P1 | P4 => P13 | P5 => P7 | P6 => P3 | P7 => P6 | P8 => P10 | P9 => P12 | P10 => P0 | P11 => P4 | P12 => P8 | P13 => P14 | P14 => P2 end.
Definition fl46_49 (l:Line) := match l with L0 => L29 | L1 => L11 | L2 => L22 | L3 => L34 | L4 => L5 | L5 => L24 | L6 => L14 | L7 => L21 | L8 => L4 | L9 => L18 | L10 => L33 | L11 => L23 | L12 => L10 | L13 => L2 | L14 => L17 | L15 => L12 | L16 => L27 | L17 => L28 | L18 => L30 | L19 => L0 | L20 => L8 | L21 => L9 | L22 => L7 | L23 => L16 | L24 => L25 | L25 => L6 | L26 => L32 | L27 => L13 | L28 => L31 | L29 => L26 | L30 => L3 | L31 => L15 | L32 => L19 | L33 => L20 | L34 => L1 end.

(* P49 : S1 S14 S17 S27 S32 S47 S52 ->
   P50 : S1 S14 S19 S24 S39 S42 S53  *)
Definition fp49_50 (p:Point) := match p with P0 => P3 | P1 => P14 | P2 => P10 | P3 => P0 | P4 => P4 | P5 => P13 | P6 => P9 | P7 => P7 | P8 => P11 | P9 => P6 | P10 => P2 | P11 => P8 | P12 => P12 | P13 => P5 | P14 => P1 end.
Definition fl49_50 (l:Line) := match l with L0 => L19 | L1 => L1 | L2 => L21 | L3 => L22 | L4 => L15 | L5 => L20 | L6 => L12 | L7 => L23 | L8 => L14 | L9 => L9 | L10 => L31 | L11 => L27 | L12 => L6 | L13 => L13 | L14 => L8 | L15 => L4 | L16 => L30 | L17 => L25 | L18 => L34 | L19 => L0 | L20 => L5 | L21 => L2 | L22 => L3 | L23 => L7 | L24 => L24 | L25 => L17 | L26 => L26 | L27 => L11 | L28 => L28 | L29 => L32 | L30 => L16 | L31 => L10 | L32 => L29 | L33 => L33 | L34 => L18 end.

(* P50 : S1 S14 S19 S24 S39 S42 S53 ->
   P53 : S1 S14 S20 S31 S34 S43 S49  *)
Definition fp50_53 (p:Point) := match p with P0 => P4 | P1 => P12 | P2 => P7 | P3 => P0 | P4 => P3 | P5 => P11 | P6 => P8 | P7 => P10 | P8 => P13 | P9 => P5 | P10 => P2 | P11 => P9 | P12 => P14 | P13 => P6 | P14 => P1 end.
Definition fl50_53 (l:Line) := match l with L0 => L26 | L1 => L1 | L2 => L24 | L3 => L25 | L4 => L17 | L5 => L23 | L6 => L7 | L7 => L20 | L8 => L16 | L9 => L9 | L10 => L30 | L11 => L33 | L12 => L5 | L13 => L13 | L14 => L10 | L15 => L3 | L16 => L31 | L17 => L22 | L18 => L28 | L19 => L0 | L20 => L6 | L21 => L2 | L22 => L4 | L23 => L12 | L24 => L21 | L25 => L15 | L26 => L19 | L27 => L11 | L28 => L34 | L29 => L29 | L30 => L14 | L31 => L8 | L32 => L32 | L33 => L27 | L34 => L18 end.

(* P53 : S1 S14 S20 S31 S34 S43 S49 ->
   P55 : S1 S15 S17 S30 S34 S40 S53  *)
Definition fp53_55 (p:Point) := match p with P0 => P13 | P1 => P6 | P2 => P8 | P3 => P1 | P4 => P11 | P5 => P4 | P6 => P10 | P7 => P9 | P8 => P3 | P9 => P12 | P10 => P2 | P11 => P7 | P12 => P5 | P13 => P14 | P14 => P0 end.
Definition fl53_55 (l:Line) := match l with L0 => L32 | L1 => L11 | L2 => L25 | L3 => L21 | L4 => L16 | L5 => L28 | L6 => L6 | L7 => L34 | L8 => L15 | L9 => L2 | L10 => L33 | L11 => L31 | L12 => L7 | L13 => L18 | L14 => L3 | L15 => L8 | L16 => L27 | L17 => L24 | L18 => L20 | L19 => L0 | L20 => L12 | L21 => L9 | L22 => L10 | L23 => L5 | L24 => L22 | L25 => L14 | L26 => L29 | L27 => L1 | L28 => L23 | L29 => L26 | L30 => L17 | L31 => L4 | L32 => L19 | L33 => L30 | L34 => L13 end.

(* P55 : S1 S15 S17 S30 S34 S40 S53 ->
   P57 : S1 S15 S18 S31 S32 S44 S51  *)
Definition fp55_57 (p:Point) := match p with P0 => P6 | P1 => P8 | P2 => P13 | P3 => P7 | P4 => P14 | P5 => P0 | P6 => P5 | P7 => P10 | P8 => P11 | P9 => P1 | P10 => P4 | P11 => P2 | P12 => P3 | P13 => P9 | P14 => P12 end.
Definition fl55_57 (l:Line) := match l with L0 => L32 | L1 => L31 | L2 => L2 | L3 => L34 | L4 => L7 | L5 => L15 | L6 => L33 | L7 => L27 | L8 => L24 | L9 => L20 | L10 => L8 | L11 => L18 | L12 => L3 | L13 => L25 | L14 => L16 | L15 => L28 | L16 => L21 | L17 => L6 | L18 => L11 | L19 => L26 | L20 => L22 | L21 => L10 | L22 => L13 | L23 => L9 | L24 => L14 | L25 => L23 | L26 => L19 | L27 => L5 | L28 => L4 | L29 => L0 | L30 => L1 | L31 => L30 | L32 => L29 | L33 => L12 | L34 => L17 end.

(* P57 : S1 S15 S18 S31 S32 S44 S51 ->
   P58 : S1 S15 S20 S27 S33 S42 S54  *)
Definition fp57_58 (p:Point) := match p with P0 => P6 | P1 => P8 | P2 => P13 | P3 => P7 | P4 => P14 | P5 => P0 | P6 => P5 | P7 => P10 | P8 => P11 | P9 => P1 | P10 => P4 | P11 => P2 | P12 => P3 | P13 => P9 | P14 => P12 end.
Definition fl57_58 (l:Line) := match l with L0 => L32 | L1 => L31 | L2 => L2 | L3 => L34 | L4 => L7 | L5 => L15 | L6 => L33 | L7 => L27 | L8 => L24 | L9 => L20 | L10 => L8 | L11 => L18 | L12 => L3 | L13 => L25 | L14 => L16 | L15 => L28 | L16 => L21 | L17 => L6 | L18 => L11 | L19 => L26 | L20 => L22 | L21 => L10 | L22 => L13 | L23 => L9 | L24 => L14 | L25 => L23 | L26 => L19 | L27 => L5 | L28 => L4 | L29 => L0 | L30 => L1 | L31 => L30 | L32 => L29 | L33 => L12 | L34 => L17 end.

(* P58 : S1 S15 S20 S27 S33 S42 S54 ->
   P60 : S2 S9 S18 S29 S38 S44 S49  *)
Definition fp58_60 (p:Point) := match p with P0 => P4 | P1 => P14 | P2 => P9 | P3 => P0 | P4 => P3 | P5 => P13 | P6 => P10 | P7 => P8 | P8 => P11 | P9 => P5 | P10 => P2 | P11 => P7 | P12 => P12 | P13 => P6 | P14 => P1 end.
Definition fl58_60 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L24 | L4 => L17 | L5 => L26 | L6 => L7 | L7 => L19 | L8 => L14 | L9 => L9 | L10 => L27 | L11 => L31 | L12 => L6 | L13 => L18 | L14 => L10 | L15 => L4 | L16 => L33 | L17 => L21 | L18 => L29 | L19 => L0 | L20 => L5 | L21 => L2 | L22 => L3 | L23 => L12 | L24 => L22 | L25 => L15 | L26 => L20 | L27 => L11 | L28 => L32 | L29 => L28 | L30 => L16 | L31 => L8 | L32 => L34 | L33 => L30 | L34 => L13 end.

(* P60 : S2 S9 S18 S29 S38 S44 S49 ->
   P62 : S2 S9 S19 S24 S36 S45 S54  *)
Definition fp60_62 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P12 | P4 => P13 | P5 => P11 | P6 => P14 | P7 => P6 | P8 => P3 | P9 => P5 | P10 => P4 | P11 => P9 | P12 => P8 | P13 => P10 | P14 => P7 end.
Definition fl60_62 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L15 | L4 => L17 | L5 => L18 | L6 => L13 | L7 => L6 | L8 => L1 | L9 => L3 | L10 => L2 | L11 => L4 | L12 => L5 | L13 => L7 | L14 => L10 | L15 => L9 | L16 => L8 | L17 => L11 | L18 => L12 | L19 => L26 | L20 => L20 | L21 => L30 | L22 => L33 | L23 => L28 | L24 => L21 | L25 => L25 | L26 => L32 | L27 => L22 | L28 => L34 | L29 => L29 | L30 => L24 | L31 => L31 | L32 => L19 | L33 => L27 | L34 => L23 end.

(* P62 : S2 S9 S19 S24 S36 S45 S54 ->
   P65 : S2 S9 S23 S30 S35 S40 S52  *)
Definition fp62_65 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P12 | P4 => P13 | P5 => P14 | P6 => P11 | P7 => P9 | P8 => P8 | P9 => P7 | P10 => P10 | P11 => P6 | P12 => P3 | P13 => P4 | P14 => P5 end.
Definition fl62_65 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L18 | L4 => L13 | L5 => L15 | L6 => L17 | L7 => L11 | L8 => L8 | L9 => L12 | L10 => L10 | L11 => L7 | L12 => L9 | L13 => L4 | L14 => L2 | L15 => L5 | L16 => L1 | L17 => L6 | L18 => L3 | L19 => L30 | L20 => L20 | L21 => L26 | L22 => L33 | L23 => L28 | L24 => L32 | L25 => L25 | L26 => L21 | L27 => L27 | L28 => L23 | L29 => L31 | L30 => L19 | L31 => L29 | L32 => L24 | L33 => L22 | L34 => L34 end.

(* P65 : S2 S9 S23 S30 S35 S40 S52 ->
   P66 : S2 S10 S16 S29 S33 S47 S52  *)
Definition fp65_66 (p:Point) := match p with P0 => P7 | P1 => P13 | P2 => P5 | P3 => P10 | P4 => P2 | P5 => P4 | P6 => P12 | P7 => P14 | P8 => P6 | P9 => P0 | P10 => P8 | P11 => P3 | P12 => P11 | P13 => P9 | P14 => P1 end.
Definition fl65_66 (l:Line) := match l with L0 => L28 | L1 => L13 | L2 => L26 | L3 => L31 | L4 => L3 | L5 => L22 | L6 => L10 | L7 => L16 | L8 => L32 | L9 => L11 | L10 => L6 | L11 => L21 | L12 => L25 | L13 => L27 | L14 => L12 | L15 => L30 | L16 => L29 | L17 => L17 | L18 => L2 | L19 => L8 | L20 => L34 | L21 => L4 | L22 => L19 | L23 => L0 | L24 => L15 | L25 => L18 | L26 => L14 | L27 => L7 | L28 => L23 | L29 => L1 | L30 => L24 | L31 => L9 | L32 => L33 | L33 => L5 | L34 => L20 end.

(* P66 : S2 S10 S16 S29 S33 S47 S52 ->
   P69 : S2 S10 S21 S30 S36 S43 S49  *)
Definition fp66_69 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl66_69 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P69 : S2 S10 S21 S30 S36 S43 S49 ->
   P70 : S2 S10 S23 S24 S39 S44 S51  *)
Definition fp69_70 (p:Point) := match p with P0 => P12 | P1 => P3 | P2 => P8 | P3 => P1 | P4 => P14 | P5 => P5 | P6 => P10 | P7 => P13 | P8 => P2 | P9 => P9 | P10 => P6 | P11 => P11 | P12 => P0 | P13 => P7 | P14 => P4 end.
Definition fl69_70 (l:Line) := match l with L0 => L20 | L1 => L9 | L2 => L30 | L3 => L16 | L4 => L33 | L5 => L5 | L6 => L26 | L7 => L19 | L8 => L15 | L9 => L1 | L10 => L21 | L11 => L22 | L12 => L12 | L13 => L32 | L14 => L24 | L15 => L8 | L16 => L3 | L17 => L27 | L18 => L18 | L19 => L7 | L20 => L0 | L21 => L10 | L22 => L11 | L23 => L23 | L24 => L14 | L25 => L31 | L26 => L6 | L27 => L17 | L28 => L28 | L29 => L29 | L30 => L2 | L31 => L25 | L32 => L13 | L33 => L4 | L34 => L34 end.

(* P70 : S2 S10 S23 S24 S39 S44 S51 ->
   P72 : S2 S12 S18 S25 S36 S47 S51  *)
Definition fp70_72 (p:Point) := match p with P0 => P13 | P1 => P5 | P2 => P7 | P3 => P8 | P4 => P6 | P5 => P14 | P6 => P0 | P7 => P9 | P8 => P3 | P9 => P11 | P10 => P1 | P11 => P2 | P12 => P12 | P13 => P4 | P14 => P10 end.
Definition fl70_72 (l:Line) := match l with L0 => L28 | L1 => L32 | L2 => L6 | L3 => L21 | L4 => L11 | L5 => L16 | L6 => L25 | L7 => L2 | L8 => L12 | L9 => L30 | L10 => L29 | L11 => L17 | L12 => L27 | L13 => L10 | L14 => L13 | L15 => L3 | L16 => L26 | L17 => L31 | L18 => L22 | L19 => L8 | L20 => L20 | L21 => L24 | L22 => L18 | L23 => L34 | L24 => L15 | L25 => L7 | L26 => L33 | L27 => L19 | L28 => L23 | L29 => L14 | L30 => L9 | L31 => L4 | L32 => L1 | L33 => L5 | L34 => L0 end.

(* P72 : S2 S12 S18 S25 S36 S47 S51 ->
   P75 : S2 S12 S19 S29 S39 S40 S50  *)
Definition fp72_75 (p:Point) := match p with P0 => P9 | P1 => P4 | P2 => P14 | P3 => P7 | P4 => P1 | P5 => P12 | P6 => P6 | P7 => P3 | P8 => P13 | P9 => P0 | P10 => P10 | P11 => P11 | P12 => P5 | P13 => P8 | P14 => P2 end.
Definition fl72_75 (l:Line) := match l with L0 => L23 | L1 => L10 | L2 => L33 | L3 => L21 | L4 => L4 | L5 => L29 | L6 => L18 | L7 => L7 | L8 => L25 | L9 => L17 | L10 => L1 | L11 => L24 | L12 => L26 | L13 => L19 | L14 => L14 | L15 => L31 | L16 => L27 | L17 => L9 | L18 => L6 | L19 => L13 | L20 => L28 | L21 => L3 | L22 => L22 | L23 => L0 | L24 => L11 | L25 => L8 | L26 => L12 | L27 => L16 | L28 => L20 | L29 => L5 | L30 => L30 | L31 => L15 | L32 => L32 | L33 => L2 | L34 => L34 end.

(* P75 : S2 S12 S19 S29 S39 S40 S50 ->
   P76 : S2 S12 S23 S26 S33 S43 S54  *)
Definition fp75_76 (p:Point) := match p with P0 => P14 | P1 => P4 | P2 => P9 | P3 => P11 | P4 => P2 | P5 => P8 | P6 => P5 | P7 => P3 | P8 => P10 | P9 => P0 | P10 => P13 | P11 => P7 | P12 => P6 | P13 => P12 | P14 => P1 end.
Definition fl75_76 (l:Line) := match l with L0 => L23 | L1 => L14 | L2 => L27 | L3 => L19 | L4 => L6 | L5 => L31 | L6 => L9 | L7 => L17 | L8 => L25 | L9 => L7 | L10 => L1 | L11 => L26 | L12 => L24 | L13 => L21 | L14 => L10 | L15 => L29 | L16 => L33 | L17 => L18 | L18 => L4 | L19 => L11 | L20 => L34 | L21 => L5 | L22 => L22 | L23 => L0 | L24 => L13 | L25 => L16 | L26 => L15 | L27 => L8 | L28 => L20 | L29 => L3 | L30 => L32 | L31 => L12 | L32 => L30 | L33 => L2 | L34 => L28 end.

(* P76 : S2 S12 S23 S26 S33 S43 S54 ->
   P79 : S2 S14 S16 S26 S39 S45 S49  *)
Definition fp76_79 (p:Point) := match p with P0 => P4 | P1 => P9 | P2 => P14 | P3 => P0 | P4 => P3 | P5 => P10 | P6 => P13 | P7 => P6 | P8 => P1 | P9 => P12 | P10 => P7 | P11 => P5 | P12 => P2 | P13 => P11 | P14 => P8 end.
Definition fl76_79 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L7 | L4 => L26 | L5 => L17 | L6 => L24 | L7 => L21 | L8 => L10 | L9 => L18 | L10 => L33 | L11 => L29 | L12 => L4 | L13 => L31 | L14 => L27 | L15 => L6 | L16 => L14 | L17 => L19 | L18 => L9 | L19 => L3 | L20 => L0 | L21 => L5 | L22 => L2 | L23 => L20 | L24 => L12 | L25 => L22 | L26 => L15 | L27 => L8 | L28 => L34 | L29 => L30 | L30 => L13 | L31 => L32 | L32 => L11 | L33 => L16 | L34 => L28 end.

(* P79 : S2 S14 S16 S26 S39 S45 S49 ->
   P81 : S2 S14 S19 S25 S38 S43 S52  *)
Definition fp79_81 (p:Point) := match p with P0 => P6 | P1 => P10 | P2 => P11 | P3 => P9 | P4 => P12 | P5 => P0 | P6 => P5 | P7 => P1 | P8 => P4 | P9 => P8 | P10 => P13 | P11 => P7 | P12 => P14 | P13 => P2 | P14 => P3 end.
Definition fl79_81 (l:Line) := match l with L0 => L34 | L1 => L33 | L2 => L2 | L3 => L7 | L4 => L32 | L5 => L31 | L6 => L15 | L7 => L30 | L8 => L25 | L9 => L19 | L10 => L8 | L11 => L13 | L12 => L4 | L13 => L11 | L14 => L22 | L15 => L29 | L16 => L14 | L17 => L5 | L18 => L24 | L19 => L21 | L20 => L23 | L21 => L18 | L22 => L10 | L23 => L20 | L24 => L26 | L25 => L16 | L26 => L9 | L27 => L1 | L28 => L0 | L29 => L3 | L30 => L6 | L31 => L12 | L32 => L17 | L33 => L27 | L34 => L28 end.

(* P81 : S2 S14 S19 S25 S38 S43 S52 ->
   P82 : S2 S14 S21 S24 S35 S47 S50  *)
Definition fp81_82 (p:Point) := match p with P0 => P6 | P1 => P10 | P2 => P11 | P3 => P9 | P4 => P12 | P5 => P0 | P6 => P5 | P7 => P1 | P8 => P4 | P9 => P8 | P10 => P13 | P11 => P7 | P12 => P14 | P13 => P2 | P14 => P3 end.
Definition fl81_82 (l:Line) := match l with L0 => L34 | L1 => L33 | L2 => L2 | L3 => L7 | L4 => L32 | L5 => L31 | L6 => L15 | L7 => L30 | L8 => L25 | L9 => L19 | L10 => L8 | L11 => L13 | L12 => L4 | L13 => L11 | L14 => L22 | L15 => L29 | L16 => L14 | L17 => L5 | L18 => L24 | L19 => L21 | L20 => L23 | L21 => L18 | L22 => L10 | L23 => L20 | L24 => L26 | L25 => L16 | L26 => L9 | L27 => L1 | L28 => L0 | L29 => L3 | L30 => L6 | L31 => L12 | L32 => L17 | L33 => L27 | L34 => L28 end.

(* P82 : S2 S14 S21 S24 S35 S47 S50 ->
   P84 : S2 S15 S16 S25 S35 S44 S54  *)
Definition fp82_84 (p:Point) := match p with P0 => P14 | P1 => P4 | P2 => P9 | P3 => P6 | P4 => P7 | P5 => P1 | P6 => P12 | P7 => P2 | P8 => P11 | P9 => P5 | P10 => P8 | P11 => P3 | P12 => P10 | P13 => P0 | P14 => P13 end.
Definition fl82_84 (l:Line) := match l with L0 => L23 | L1 => L31 | L2 => L9 | L3 => L14 | L4 => L27 | L5 => L19 | L6 => L6 | L7 => L26 | L8 => L24 | L9 => L25 | L10 => L17 | L11 => L1 | L12 => L7 | L13 => L18 | L14 => L21 | L15 => L33 | L16 => L4 | L17 => L10 | L18 => L29 | L19 => L32 | L20 => L34 | L21 => L2 | L22 => L15 | L23 => L28 | L24 => L22 | L25 => L3 | L26 => L13 | L27 => L11 | L28 => L0 | L29 => L12 | L30 => L8 | L31 => L16 | L32 => L5 | L33 => L30 | L34 => L20 end.

(* P84 : S2 S15 S16 S25 S35 S44 S54 ->
   P87 : S2 S15 S18 S30 S33 S45 S50  *)
Definition fp84_87 (p:Point) := match p with P0 => P4 | P1 => P14 | P2 => P9 | P3 => P0 | P4 => P3 | P5 => P13 | P6 => P10 | P7 => P5 | P8 => P2 | P9 => P8 | P10 => P11 | P11 => P6 | P12 => P1 | P13 => P7 | P14 => P12 end.
Definition fl84_87 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L17 | L4 => L24 | L5 => L7 | L6 => L26 | L7 => L19 | L8 => L14 | L9 => L9 | L10 => L27 | L11 => L31 | L12 => L6 | L13 => L29 | L14 => L33 | L15 => L4 | L16 => L10 | L17 => L21 | L18 => L18 | L19 => L5 | L20 => L0 | L21 => L3 | L22 => L2 | L23 => L20 | L24 => L15 | L25 => L22 | L26 => L12 | L27 => L16 | L28 => L28 | L29 => L32 | L30 => L11 | L31 => L30 | L32 => L13 | L33 => L8 | L34 => L34 end.

(* P87 : S2 S15 S18 S30 S33 S45 S50 ->
   P88 : S2 S15 S21 S26 S38 S40 S51  *)
Definition fp87_88 (p:Point) := match p with P0 => P4 | P1 => P14 | P2 => P9 | P3 => P3 | P4 => P0 | P5 => P10 | P6 => P13 | P7 => P11 | P8 => P8 | P9 => P2 | P10 => P5 | P11 => P7 | P12 => P12 | P13 => P6 | P14 => P1 end.
Definition fl87_88 (l:Line) := match l with L0 => L23 | L1 => L1 | L2 => L25 | L3 => L24 | L4 => L17 | L5 => L26 | L6 => L7 | L7 => L6 | L8 => L27 | L9 => L9 | L10 => L14 | L11 => L31 | L12 => L19 | L13 => L29 | L14 => L10 | L15 => L21 | L16 => L33 | L17 => L4 | L18 => L18 | L19 => L12 | L20 => L20 | L21 => L15 | L22 => L22 | L23 => L0 | L24 => L3 | L25 => L2 | L26 => L5 | L27 => L8 | L28 => L34 | L29 => L13 | L30 => L30 | L31 => L11 | L32 => L32 | L33 => L16 | L34 => L28 end.

(* P88 : S2 S15 S21 S26 S38 S40 S51 ->
   P91 : S3 S8 S18 S31 S36 S45 S49  *)
Definition fp88_91 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P7 | P8 => P8 | P9 => P10 | P10 => P9 | P11 => P11 | P12 => P12 | P13 => P14 | P14 => P13 end.
Definition fl88_91 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L3 | L4 => L4 | L5 => L5 | L6 => L6 | L7 => L17 | L8 => L18 | L9 => L16 | L10 => L13 | L11 => L14 | L12 => L15 | L13 => L10 | L14 => L11 | L15 => L12 | L16 => L9 | L17 => L7 | L18 => L8 | L19 => L21 | L20 => L20 | L21 => L19 | L22 => L22 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L32 | L28 => L31 | L29 => L34 | L30 => L33 | L31 => L28 | L32 => L27 | L33 => L30 | L34 => L29 end.

(* P91 : S3 S8 S18 S31 S36 S45 S49 ->
   P93 : S3 S8 S21 S28 S35 S40 S55  *)
Definition fp91_93 (p:Point) := match p with P0 => P4 | P1 => P10 | P2 => P13 | P3 => P3 | P4 => P0 | P5 => P14 | P6 => P9 | P7 => P11 | P8 => P8 | P9 => P6 | P10 => P1 | P11 => P7 | P12 => P12 | P13 => P2 | P14 => P5 end.
Definition fl91_93 (l:Line) := match l with L0 => L25 | L1 => L1 | L2 => L23 | L3 => L24 | L4 => L7 | L5 => L26 | L6 => L17 | L7 => L4 | L8 => L8 | L9 => L30 | L10 => L34 | L11 => L13 | L12 => L19 | L13 => L11 | L14 => L28 | L15 => L21 | L16 => L16 | L17 => L6 | L18 => L32 | L19 => L12 | L20 => L20 | L21 => L15 | L22 => L22 | L23 => L2 | L24 => L3 | L25 => L0 | L26 => L5 | L27 => L27 | L28 => L14 | L29 => L31 | L30 => L9 | L31 => L29 | L32 => L18 | L33 => L33 | L34 => L10 end.

(* P93 : S3 S8 S21 S28 S35 S40 S55 ->
   P94 : S3 S8 S23 S27 S33 S46 S52  *)
Definition fp93_94 (p:Point) := match p with P0 => P3 | P1 => P8 | P2 => P12 | P3 => P4 | P4 => P0 | P5 => P11 | P6 => P7 | P7 => P14 | P8 => P10 | P9 => P5 | P10 => P1 | P11 => P9 | P12 => P13 | P13 => P2 | P14 => P6 end.
Definition fl93_94 (l:Line) := match l with L0 => L20 | L1 => L1 | L2 => L22 | L3 => L19 | L4 => L12 | L5 => L21 | L6 => L15 | L7 => L3 | L8 => L8 | L9 => L32 | L10 => L27 | L11 => L18 | L12 => L24 | L13 => L9 | L14 => L33 | L15 => L26 | L16 => L16 | L17 => L5 | L18 => L30 | L19 => L7 | L20 => L25 | L21 => L17 | L22 => L23 | L23 => L2 | L24 => L4 | L25 => L0 | L26 => L6 | L27 => L34 | L28 => L14 | L29 => L29 | L30 => L11 | L31 => L31 | L32 => L13 | L33 => L28 | L34 => L10 end.

(* P94 : S3 S8 S23 S27 S33 S46 S52 ->
   P96 : S3 S11 S16 S28 S33 S45 S54  *)
Definition fp94_96 (p:Point) := match p with P0 => P10 | P1 => P13 | P2 => P4 | P3 => P6 | P4 => P11 | P5 => P8 | P6 => P1 | P7 => P2 | P8 => P7 | P9 => P12 | P10 => P5 | P11 => P3 | P12 => P14 | P13 => P9 | P14 => P0 end.
Definition fl94_96 (l:Line) := match l with L0 => L25 | L1 => L34 | L2 => L8 | L3 => L13 | L4 => L30 | L5 => L19 | L6 => L4 | L7 => L11 | L8 => L28 | L9 => L6 | L10 => L16 | L11 => L21 | L12 => L32 | L13 => L17 | L14 => L1 | L15 => L7 | L16 => L23 | L17 => L24 | L18 => L26 | L19 => L2 | L20 => L31 | L21 => L33 | L22 => L15 | L23 => L5 | L24 => L22 | L25 => L29 | L26 => L14 | L27 => L3 | L28 => L18 | L29 => L20 | L30 => L27 | L31 => L0 | L32 => L10 | L33 => L9 | L34 => L12 end.

(* P96 : S3 S11 S16 S28 S33 S45 S54 ->
   P99 : S3 S11 S17 S29 S38 S40 S52  *)
Definition fp96_99 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P12 | P4 => P14 | P5 => P11 | P6 => P13 | P7 => P10 | P8 => P8 | P9 => P9 | P10 => P7 | P11 => P5 | P12 => P3 | P13 => P6 | P14 => P4 end.
Definition fl96_99 (l:Line) := match l with L0 => L0 | L1 => L9 | L2 => L11 | L3 => L8 | L4 => L10 | L5 => L12 | L6 => L7 | L7 => L6 | L8 => L3 | L9 => L1 | L10 => L4 | L11 => L2 | L12 => L5 | L13 => L13 | L14 => L17 | L15 => L16 | L16 => L15 | L17 => L14 | L18 => L18 | L19 => L26 | L20 => L20 | L21 => L33 | L22 => L30 | L23 => L23 | L24 => L27 | L25 => L31 | L26 => L19 | L27 => L24 | L28 => L34 | L29 => L29 | L30 => L22 | L31 => L25 | L32 => L32 | L33 => L21 | L34 => L28 end.

(* P99 : S3 S11 S17 S29 S38 S40 S52 ->
   P100 : S3 S11 S21 S24 S36 S46 S51  *)
Definition fp99_100 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P8 | P4 => P9 | P5 => P7 | P6 => P10 | P7 => P13 | P8 => P12 | P9 => P14 | P10 => P11 | P11 => P6 | P12 => P3 | P13 => P5 | P14 => P4 end.
Definition fl99_100 (l:Line) := match l with L0 => L0 | L1 => L18 | L2 => L13 | L3 => L16 | L4 => L14 | L5 => L15 | L6 => L17 | L7 => L4 | L8 => L5 | L9 => L1 | L10 => L6 | L11 => L2 | L12 => L3 | L13 => L11 | L14 => L7 | L15 => L8 | L16 => L12 | L17 => L10 | L18 => L9 | L19 => L24 | L20 => L20 | L21 => L27 | L22 => L32 | L23 => L23 | L24 => L33 | L25 => L29 | L26 => L21 | L27 => L26 | L28 => L28 | L29 => L31 | L30 => L22 | L31 => L25 | L32 => L30 | L33 => L19 | L34 => L34 end.

(* P100 : S3 S11 S21 S24 S36 S46 S51 ->
   P102 : S3 S12 S17 S27 S36 S41 S54  *)
Definition fp100_102 (p:Point) := match p with P0 => P12 | P1 => P8 | P2 => P3 | P3 => P10 | P4 => P5 | P5 => P1 | P6 => P14 | P7 => P7 | P8 => P4 | P9 => P0 | P10 => P11 | P11 => P2 | P12 => P13 | P13 => P9 | P14 => P6 end.
Definition fl100_102 (l:Line) := match l with L0 => L20 | L1 => L30 | L2 => L9 | L3 => L26 | L4 => L5 | L5 => L16 | L6 => L33 | L7 => L27 | L8 => L24 | L9 => L32 | L10 => L3 | L11 => L18 | L12 => L8 | L13 => L22 | L14 => L15 | L15 => L19 | L16 => L21 | L17 => L12 | L18 => L1 | L19 => L34 | L20 => L25 | L21 => L4 | L22 => L13 | L23 => L2 | L24 => L17 | L25 => L29 | L26 => L28 | L27 => L7 | L28 => L10 | L29 => L0 | L30 => L11 | L31 => L31 | L32 => L23 | L33 => L6 | L34 => L14 end.

(* P102 : S3 S12 S17 S27 S36 S41 S54 ->
   P104 : S3 S12 S18 S29 S33 S42 S55  *)
Definition fp102_104 (p:Point) := match p with P0 => P5 | P1 => P11 | P2 => P9 | P3 => P10 | P4 => P12 | P5 => P6 | P6 => P0 | P7 => P2 | P8 => P4 | P9 => P14 | P10 => P8 | P11 => P7 | P12 => P13 | P13 => P3 | P14 => P1 end.
Definition fl102_104 (l:Line) := match l with L0 => L29 | L1 => L30 | L2 => L2 | L3 => L17 | L4 => L27 | L5 => L28 | L6 => L12 | L7 => L5 | L8 => L24 | L9 => L11 | L10 => L14 | L11 => L22 | L12 => L34 | L13 => L18 | L14 => L10 | L15 => L4 | L16 => L21 | L17 => L33 | L18 => L23 | L19 => L8 | L20 => L25 | L21 => L19 | L22 => L13 | L23 => L9 | L24 => L26 | L25 => L20 | L26 => L16 | L27 => L7 | L28 => L15 | L29 => L31 | L30 => L32 | L31 => L0 | L32 => L1 | L33 => L6 | L34 => L3 end.

(* P104 : S3 S12 S18 S29 S33 S42 S55 ->
   P107 : S3 S12 S23 S31 S34 S40 S51  *)
Definition fp104_107 (p:Point) := match p with P0 => P5 | P1 => P9 | P2 => P11 | P3 => P12 | P4 => P10 | P5 => P6 | P6 => P0 | P7 => P1 | P8 => P3 | P9 => P7 | P10 => P13 | P11 => P14 | P12 => P8 | P13 => P4 | P14 => P2 end.
Definition fl104_107 (l:Line) := match l with L0 => L29 | L1 => L30 | L2 => L2 | L3 => L12 | L4 => L28 | L5 => L27 | L6 => L17 | L7 => L4 | L8 => L21 | L9 => L18 | L10 => L10 | L11 => L23 | L12 => L33 | L13 => L11 | L14 => L14 | L15 => L5 | L16 => L24 | L17 => L34 | L18 => L22 | L19 => L16 | L20 => L20 | L21 => L26 | L22 => L9 | L23 => L13 | L24 => L19 | L25 => L25 | L26 => L8 | L27 => L15 | L28 => L7 | L29 => L31 | L30 => L32 | L31 => L0 | L32 => L1 | L33 => L3 | L34 => L6 end.

(* P107 : S3 S12 S23 S31 S34 S40 S51 ->
   P109 : S3 S13 S16 S29 S34 S46 S49  *)
Definition fp107_109 (p:Point) := match p with P0 => P8 | P1 => P3 | P2 => P12 | P3 => P14 | P4 => P5 | P5 => P10 | P6 => P1 | P7 => P0 | P8 => P7 | P9 => P4 | P10 => P11 | P11 => P13 | P12 => P6 | P13 => P9 | P14 => P2 end.
Definition fl107_109 (l:Line) := match l with L0 => L20 | L1 => L27 | L2 => L8 | L3 => L3 | L4 => L24 | L5 => L32 | L6 => L18 | L7 => L12 | L8 => L22 | L9 => L15 | L10 => L1 | L11 => L21 | L12 => L19 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L33 | L17 => L30 | L18 => L26 | L19 => L14 | L20 => L31 | L21 => L23 | L22 => L6 | L23 => L17 | L24 => L28 | L25 => L29 | L26 => L2 | L27 => L13 | L28 => L4 | L29 => L25 | L30 => L34 | L31 => L0 | L32 => L10 | L33 => L7 | L34 => L11 end.

(* P109 : S3 S13 S16 S29 S34 S46 S49 ->
   P110 : S3 S13 S18 S28 S38 S41 S51  *)
Definition fp109_110 (p:Point) := match p with P0 => P12 | P1 => P8 | P2 => P3 | P3 => P2 | P4 => P13 | P5 => P9 | P6 => P6 | P7 => P14 | P8 => P1 | P9 => P5 | P10 => P10 | P11 => P11 | P12 => P0 | P13 => P4 | P14 => P7 end.
Definition fl109_110 (l:Line) := match l with L0 => L20 | L1 => L16 | L2 => L33 | L3 => L9 | L4 => L30 | L5 => L5 | L6 => L26 | L7 => L32 | L8 => L8 | L9 => L3 | L10 => L27 | L11 => L24 | L12 => L18 | L13 => L19 | L14 => L22 | L15 => L15 | L16 => L1 | L17 => L21 | L18 => L12 | L19 => L13 | L20 => L0 | L21 => L17 | L22 => L14 | L23 => L28 | L24 => L11 | L25 => L25 | L26 => L6 | L27 => L10 | L28 => L23 | L29 => L29 | L30 => L4 | L31 => L31 | L32 => L7 | L33 => L2 | L34 => L34 end.

(* P110 : S3 S13 S18 S28 S38 S41 S51 ->
   P113 : S3 S13 S23 S24 S35 S42 S54  *)
Definition fp110_113 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl110_113 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P113 : S3 S13 S23 S24 S35 S42 S54 ->
   P115 : S3 S14 S16 S31 S35 S41 S52  *)
Definition fp113_115 (p:Point) := match p with P0 => P8 | P1 => P3 | P2 => P12 | P3 => P14 | P4 => P5 | P5 => P10 | P6 => P1 | P7 => P0 | P8 => P7 | P9 => P4 | P10 => P11 | P11 => P13 | P12 => P6 | P13 => P9 | P14 => P2 end.
Definition fl113_115 (l:Line) := match l with L0 => L20 | L1 => L27 | L2 => L8 | L3 => L3 | L4 => L24 | L5 => L32 | L6 => L18 | L7 => L12 | L8 => L22 | L9 => L15 | L10 => L1 | L11 => L21 | L12 => L19 | L13 => L5 | L14 => L16 | L15 => L9 | L16 => L33 | L17 => L30 | L18 => L26 | L19 => L14 | L20 => L31 | L21 => L23 | L22 => L6 | L23 => L17 | L24 => L28 | L25 => L29 | L26 => L2 | L27 => L13 | L28 => L4 | L29 => L25 | L30 => L34 | L31 => L0 | L32 => L10 | L33 => L7 | L34 => L11 end.

(* P115 : S3 S14 S16 S31 S35 S41 S52 ->
   P116 : S3 S14 S17 S24 S34 S45 S55  *)
Definition fp115_116 (p:Point) := match p with P0 => P10 | P1 => P4 | P2 => P13 | P3 => P7 | P4 => P2 | P5 => P12 | P6 => P5 | P7 => P11 | P8 => P6 | P9 => P8 | P10 => P1 | P11 => P3 | P12 => P14 | P13 => P0 | P14 => P9 end.
Definition fl115_116 (l:Line) := match l with L0 => L25 | L1 => L13 | L2 => L30 | L3 => L34 | L4 => L8 | L5 => L19 | L6 => L4 | L7 => L17 | L8 => L7 | L9 => L23 | L10 => L24 | L11 => L1 | L12 => L26 | L13 => L11 | L14 => L21 | L15 => L28 | L16 => L6 | L17 => L16 | L18 => L32 | L19 => L10 | L20 => L31 | L21 => L3 | L22 => L22 | L23 => L18 | L24 => L15 | L25 => L0 | L26 => L14 | L27 => L33 | L28 => L5 | L29 => L20 | L30 => L9 | L31 => L29 | L32 => L2 | L33 => L27 | L34 => L12 end.

(* P116 : S3 S14 S17 S24 S34 S45 S55 ->
   P119 : S3 S14 S21 S27 S38 S42 S49  *)
Definition fp116_119 (p:Point) := match p with P0 => P10 | P1 => P13 | P2 => P4 | P3 => P7 | P4 => P2 | P5 => P5 | P6 => P12 | P7 => P3 | P8 => P14 | P9 => P9 | P10 => P0 | P11 => P11 | P12 => P6 | P13 => P1 | P14 => P8 end.
Definition fl116_119 (l:Line) := match l with L0 => L25 | L1 => L13 | L2 => L30 | L3 => L19 | L4 => L4 | L5 => L34 | L6 => L8 | L7 => L16 | L8 => L6 | L9 => L32 | L10 => L21 | L11 => L11 | L12 => L28 | L13 => L1 | L14 => L24 | L15 => L26 | L16 => L7 | L17 => L17 | L18 => L23 | L19 => L3 | L20 => L31 | L21 => L10 | L22 => L22 | L23 => L18 | L24 => L14 | L25 => L0 | L26 => L15 | L27 => L27 | L28 => L12 | L29 => L29 | L30 => L2 | L31 => L20 | L32 => L9 | L33 => L33 | L34 => L5 end.

(* P119 : S3 S14 S21 S27 S38 S42 S49 ->
   P120 : S4 S8 S19 S25 S36 S46 S53  *)
Definition fp119_120 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P3 | P4 => P4 | P5 => P5 | P6 => P6 | P7 => P14 | P8 => P13 | P9 => P12 | P10 => P11 | P11 => P10 | P12 => P9 | P13 => P8 | P14 => P7 end.
Definition fl119_120 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L6 | L4 => L5 | L5 => L4 | L6 => L3 | L7 => L7 | L8 => L11 | L9 => L10 | L10 => L9 | L11 => L8 | L12 => L12 | L13 => L14 | L14 => L13 | L15 => L15 | L16 => L18 | L17 => L17 | L18 => L16 | L19 => L22 | L20 => L21 | L21 => L20 | L22 => L19 | L23 => L26 | L24 => L25 | L25 => L24 | L26 => L23 | L27 => L28 | L28 => L27 | L29 => L30 | L30 => L29 | L31 => L31 | L32 => L32 | L33 => L33 | L34 => L34 end.

(* P120 : S4 S8 S19 S25 S36 S46 S53 ->
   P123 : S4 S8 S22 S26 S33 S45 S55  *)
Definition fp120_123 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl120_123 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P123 : S4 S8 S22 S26 S33 S45 S55 ->
   P125 : S4 S8 S23 S31 S35 S44 S48  *)
Definition fp123_125 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P14 | P4 => P11 | P5 => P13 | P6 => P12 | P7 => P5 | P8 => P4 | P9 => P6 | P10 => P3 | P11 => P8 | P12 => P9 | P13 => P7 | P14 => P10 end.
Definition fl123_125 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L17 | L4 => L15 | L5 => L18 | L6 => L13 | L7 => L5 | L8 => L1 | L9 => L4 | L10 => L2 | L11 => L3 | L12 => L6 | L13 => L12 | L14 => L8 | L15 => L9 | L16 => L10 | L17 => L11 | L18 => L7 | L19 => L19 | L20 => L23 | L21 => L31 | L22 => L27 | L23 => L34 | L24 => L24 | L25 => L22 | L26 => L29 | L27 => L25 | L28 => L28 | L29 => L32 | L30 => L21 | L31 => L30 | L32 => L26 | L33 => L33 | L34 => L20 end.

(* P125 : S4 S8 S23 S31 S35 S44 S48 ->
   P126 : S4 S10 S17 S29 S32 S44 S55  *)
Definition fp125_126 (p:Point) := match p with P0 => P13 | P1 => P9 | P2 => P3 | P3 => P6 | P4 => P8 | P5 => P12 | P6 => P2 | P7 => P1 | P8 => P11 | P9 => P7 | P10 => P5 | P11 => P4 | P12 => P10 | P13 => P14 | P14 => P0 end.
Definition fl125_126 (l:Line) := match l with L0 => L21 | L1 => L32 | L2 => L16 | L3 => L11 | L4 => L28 | L5 => L25 | L6 => L6 | L7 => L18 | L8 => L29 | L9 => L4 | L10 => L10 | L11 => L23 | L12 => L33 | L13 => L12 | L14 => L1 | L15 => L15 | L16 => L19 | L17 => L20 | L18 => L22 | L19 => L2 | L20 => L34 | L21 => L31 | L22 => L7 | L23 => L3 | L24 => L24 | L25 => L27 | L26 => L8 | L27 => L5 | L28 => L9 | L29 => L26 | L30 => L30 | L31 => L0 | L32 => L14 | L33 => L13 | L34 => L17 end.

(* P126 : S4 S10 S17 S29 S32 S44 S55 ->
   P129 : S4 S10 S20 S31 S36 S41 S51  *)
Definition fp126_129 (p:Point) := match p with P0 => P6 | P1 => P14 | P2 => P7 | P3 => P13 | P4 => P8 | P5 => P0 | P6 => P5 | P7 => P10 | P8 => P11 | P9 => P3 | P10 => P2 | P11 => P4 | P12 => P1 | P13 => P9 | P14 => P12 end.
Definition fl126_129 (l:Line) := match l with L0 => L31 | L1 => L32 | L2 => L2 | L3 => L34 | L4 => L15 | L5 => L7 | L6 => L33 | L7 => L27 | L8 => L14 | L9 => L9 | L10 => L19 | L11 => L23 | L12 => L6 | L13 => L13 | L14 => L26 | L15 => L28 | L16 => L10 | L17 => L3 | L18 => L22 | L19 => L16 | L20 => L11 | L21 => L21 | L22 => L25 | L23 => L20 | L24 => L24 | L25 => L18 | L26 => L8 | L27 => L5 | L28 => L4 | L29 => L1 | L30 => L0 | L31 => L30 | L32 => L29 | L33 => L12 | L34 => L17 end.

(* P129 : S4 S10 S20 S31 S36 S41 S51 ->
   P130 : S4 S10 S23 S30 S33 S42 S53  *)
Definition fp129_130 (p:Point) := match p with P0 => P6 | P1 => P7 | P2 => P14 | P3 => P8 | P4 => P13 | P5 => P0 | P6 => P5 | P7 => P12 | P8 => P9 | P9 => P4 | P10 => P1 | P11 => P3 | P12 => P2 | P13 => P11 | P14 => P10 end.
Definition fl129_130 (l:Line) := match l with L0 => L31 | L1 => L32 | L2 => L2 | L3 => L33 | L4 => L7 | L5 => L15 | L6 => L34 | L7 => L28 | L8 => L10 | L9 => L13 | L10 => L26 | L11 => L22 | L12 => L3 | L13 => L9 | L14 => L19 | L15 => L27 | L16 => L14 | L17 => L6 | L18 => L23 | L19 => L8 | L20 => L18 | L21 => L24 | L22 => L20 | L23 => L25 | L24 => L21 | L25 => L11 | L26 => L16 | L27 => L4 | L28 => L5 | L29 => L1 | L30 => L0 | L31 => L30 | L32 => L29 | L33 => L17 | L34 => L12 end.

(* P130 : S4 S10 S23 S30 S33 S42 S53 ->
   P133 : S4 S11 S17 S30 S36 S45 S48  *)
Definition fp130_133 (p:Point) := match p with P0 => P11 | P1 => P8 | P2 => P4 | P3 => P10 | P4 => P6 | P5 => P1 | P6 => P13 | P7 => P3 | P8 => P7 | P9 => P12 | P10 => P0 | P11 => P14 | P12 => P2 | P13 => P5 | P14 => P9 end.
Definition fl130_133 (l:Line) := match l with L0 => L24 | L1 => L34 | L2 => L11 | L3 => L22 | L4 => L5 | L5 => L14 | L6 => L29 | L7 => L32 | L8 => L3 | L9 => L18 | L10 => L20 | L11 => L27 | L12 => L8 | L13 => L1 | L14 => L23 | L15 => L25 | L16 => L17 | L17 => L7 | L18 => L26 | L19 => L4 | L20 => L13 | L21 => L30 | L22 => L19 | L23 => L33 | L24 => L31 | L25 => L2 | L26 => L15 | L27 => L10 | L28 => L12 | L29 => L9 | L30 => L0 | L31 => L21 | L32 => L28 | L33 => L16 | L34 => L6 end.

(* P133 : S4 S11 S17 S30 S36 S45 S48 ->
   P135 : S4 S11 S20 S29 S33 S46 S50  *)
Definition fp133_135 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl133_135 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P135 : S4 S11 S20 S29 S33 S46 S50 ->
   P136 : S4 S11 S22 S25 S38 S44 S51  *)
Definition fp135_136 (p:Point) := match p with P0 => P3 | P1 => P13 | P2 => P9 | P3 => P0 | P4 => P4 | P5 => P14 | P6 => P10 | P7 => P12 | P8 => P8 | P9 => P2 | P10 => P6 | P11 => P11 | P12 => P7 | P13 => P1 | P14 => P5 end.
Definition fl135_136 (l:Line) := match l with L0 => L21 | L1 => L1 | L2 => L19 | L3 => L20 | L4 => L15 | L5 => L22 | L6 => L12 | L7 => L25 | L8 => L32 | L9 => L28 | L10 => L16 | L11 => L11 | L12 => L6 | L13 => L33 | L14 => L29 | L15 => L4 | L16 => L10 | L17 => L23 | L18 => L18 | L19 => L2 | L20 => L3 | L21 => L0 | L22 => L5 | L23 => L17 | L24 => L24 | L25 => L7 | L26 => L26 | L27 => L27 | L28 => L9 | L29 => L14 | L30 => L31 | L31 => L30 | L32 => L8 | L33 => L13 | L34 => L34 end.

(* P136 : S4 S11 S22 S25 S38 S44 S51 ->
   P139 : S4 S13 S19 S29 S38 S42 S48  *)
Definition fp136_139 (p:Point) := match p with P0 => P5 | P1 => P12 | P2 => P10 | P3 => P8 | P4 => P14 | P5 => P3 | P6 => P1 | P7 => P0 | P8 => P6 | P9 => P11 | P10 => P9 | P11 => P7 | P12 => P13 | P13 => P4 | P14 => P2 end.
Definition fl136_139 (l:Line) := match l with L0 => L30 | L1 => L27 | L2 => L12 | L3 => L2 | L4 => L29 | L5 => L28 | L6 => L17 | L7 => L9 | L8 => L33 | L9 => L16 | L10 => L5 | L11 => L26 | L12 => L20 | L13 => L4 | L14 => L13 | L15 => L8 | L16 => L25 | L17 => L19 | L18 => L34 | L19 => L18 | L20 => L32 | L21 => L24 | L22 => L3 | L23 => L14 | L24 => L31 | L25 => L23 | L26 => L6 | L27 => L15 | L28 => L1 | L29 => L22 | L30 => L21 | L31 => L0 | L32 => L7 | L33 => L11 | L34 => L10 end.

(* P139 : S4 S13 S19 S29 S38 S42 S48 ->
   P141 : S4 S13 S22 S30 S35 S41 S50  *)
Definition fp139_141 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl139_141 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P141 : S4 S13 S22 S30 S35 S41 S50 ->
   P142 : S4 S13 S23 S26 S32 S46 S51  *)
Definition fp141_142 (p:Point) := match p with P0 => P9 | P1 => P3 | P2 => P13 | P3 => P1 | P4 => P7 | P5 => P5 | P6 => P11 | P7 => P4 | P8 => P14 | P9 => P0 | P10 => P10 | P11 => P6 | P12 => P12 | P13 => P2 | P14 => P8 end.
Definition fl141_142 (l:Line) := match l with L0 => L21 | L1 => L10 | L2 => L29 | L3 => L23 | L4 => L4 | L5 => L33 | L6 => L18 | L7 => L22 | L8 => L19 | L9 => L20 | L10 => L1 | L11 => L15 | L12 => L12 | L13 => L25 | L14 => L32 | L15 => L11 | L16 => L16 | L17 => L28 | L18 => L6 | L19 => L8 | L20 => L9 | L21 => L0 | L22 => L7 | L23 => L3 | L24 => L31 | L25 => L13 | L26 => L26 | L27 => L27 | L28 => L17 | L29 => L2 | L30 => L30 | L31 => L24 | L32 => L14 | L33 => L5 | L34 => L34 end.

(* P142 : S4 S13 S23 S26 S32 S46 S51 ->
   P145 : S4 S14 S17 S26 S38 S41 S53  *)
Definition fp142_145 (p:Point) := match p with P0 => P12 | P1 => P10 | P2 => P5 | P3 => P6 | P4 => P9 | P5 => P11 | P6 => P0 | P7 => P2 | P8 => P13 | P9 => P7 | P10 => P4 | P11 => P3 | P12 => P8 | P13 => P14 | P14 => P1 end.
Definition fl142_145 (l:Line) := match l with L0 => L30 | L1 => L33 | L2 => L5 | L3 => L16 | L4 => L26 | L5 => L20 | L6 => L9 | L7 => L4 | L8 => L25 | L9 => L8 | L10 => L13 | L11 => L19 | L12 => L34 | L13 => L17 | L14 => L12 | L15 => L2 | L16 => L27 | L17 => L29 | L18 => L28 | L19 => L7 | L20 => L32 | L21 => L31 | L22 => L15 | L23 => L10 | L24 => L21 | L25 => L23 | L26 => L18 | L27 => L11 | L28 => L14 | L29 => L22 | L30 => L24 | L31 => L0 | L32 => L6 | L33 => L3 | L34 => L1 end.

(* P145 : S4 S14 S17 S26 S38 S41 S53 ->
   P147 : S4 S14 S19 S31 S32 S45 S50  *)
Definition fp145_147 (p:Point) := match p with P0 => P11 | P1 => P4 | P2 => P8 | P3 => P1 | P4 => P13 | P5 => P6 | P6 => P10 | P7 => P5 | P8 => P9 | P9 => P2 | P10 => P14 | P11 => P3 | P12 => P7 | P13 => P0 | P14 => P12 end.
Definition fl145_147 (l:Line) := match l with L0 => L24 | L1 => L11 | L2 => L34 | L3 => L29 | L4 => L14 | L5 => L22 | L6 => L5 | L7 => L25 | L8 => L23 | L9 => L26 | L10 => L17 | L11 => L1 | L12 => L7 | L13 => L27 | L14 => L20 | L15 => L8 | L16 => L3 | L17 => L32 | L18 => L18 | L19 => L9 | L20 => L10 | L21 => L0 | L22 => L12 | L23 => L16 | L24 => L21 | L25 => L6 | L26 => L28 | L27 => L33 | L28 => L2 | L29 => L15 | L30 => L31 | L31 => L30 | L32 => L4 | L33 => L13 | L34 => L19 end.

(* P147 : S4 S14 S19 S31 S32 S45 S50 ->
   P148 : S4 S14 S20 S25 S35 S42 S55  *)
Definition fp147_148 (p:Point) := match p with P0 => P11 | P1 => P4 | P2 => P8 | P3 => P13 | P4 => P1 | P5 => P10 | P6 => P6 | P7 => P14 | P8 => P2 | P9 => P9 | P10 => P5 | P11 => P0 | P12 => P12 | P13 => P3 | P14 => P7 end.
Definition fl147_148 (l:Line) := match l with L0 => L24 | L1 => L11 | L2 => L34 | L3 => L14 | L4 => L29 | L5 => L5 | L6 => L22 | L7 => L7 | L8 => L17 | L9 => L26 | L10 => L23 | L11 => L1 | L12 => L25 | L13 => L27 | L14 => L3 | L15 => L32 | L16 => L20 | L17 => L8 | L18 => L18 | L19 => L28 | L20 => L16 | L21 => L21 | L22 => L6 | L23 => L10 | L24 => L0 | L25 => L12 | L26 => L9 | L27 => L13 | L28 => L19 | L29 => L4 | L30 => L30 | L31 => L31 | L32 => L15 | L33 => L33 | L34 => L2 end.

(* P148 : S4 S14 S20 S25 S35 S42 S55 ->
   P151 : S5 S8 S19 S28 S39 S45 S48  *)
Definition fp148_151 (p:Point) := match p with P0 => P14 | P1 => P8 | P2 => P5 | P3 => P2 | P4 => P11 | P5 => P9 | P6 => P4 | P7 => P7 | P8 => P6 | P9 => P0 | P10 => P13 | P11 => P10 | P12 => P3 | P13 => P1 | P14 => P12 end.
Definition fl148_151 (l:Line) := match l with L0 => L27 | L1 => L14 | L2 => L23 | L3 => L31 | L4 => L6 | L5 => L19 | L6 => L9 | L7 => L24 | L8 => L32 | L9 => L20 | L10 => L3 | L11 => L8 | L12 => L18 | L13 => L28 | L14 => L30 | L15 => L17 | L16 => L12 | L17 => L29 | L18 => L2 | L19 => L16 | L20 => L15 | L21 => L0 | L22 => L13 | L23 => L5 | L24 => L34 | L25 => L11 | L26 => L22 | L27 => L33 | L28 => L10 | L29 => L4 | L30 => L21 | L31 => L26 | L32 => L7 | L33 => L1 | L34 => L25 end.

(* P151 : S5 S8 S19 S28 S39 S45 S48 ->
   P152 : S5 S8 S21 S26 S37 S46 S49  *)
Definition fp151_152 (p:Point) := match p with P0 => P5 | P1 => P14 | P2 => P8 | P3 => P7 | P4 => P13 | P5 => P6 | P6 => P0 | P7 => P9 | P8 => P11 | P9 => P4 | P10 => P2 | P11 => P1 | P12 => P3 | P13 => P12 | P14 => P10 end.
Definition fl151_152 (l:Line) := match l with L0 => L27 | L1 => L28 | L2 => L2 | L3 => L29 | L4 => L17 | L5 => L12 | L6 => L30 | L7 => L6 | L8 => L14 | L9 => L19 | L10 => L23 | L11 => L9 | L12 => L31 | L13 => L18 | L14 => L8 | L15 => L3 | L16 => L20 | L17 => L32 | L18 => L24 | L19 => L13 | L20 => L22 | L21 => L26 | L22 => L10 | L23 => L25 | L24 => L11 | L25 => L16 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L7 | L30 => L15 | L31 => L4 | L32 => L5 | L33 => L1 | L34 => L0 end.

(* P152 : S5 S8 S21 S26 S37 S46 S49 ->
   P154 : S5 S8 S22 S25 S35 S47 S52  *)
Definition fp152_154 (p:Point) := match p with P0 => P5 | P1 => P14 | P2 => P8 | P3 => P7 | P4 => P13 | P5 => P6 | P6 => P0 | P7 => P9 | P8 => P11 | P9 => P4 | P10 => P2 | P11 => P1 | P12 => P3 | P13 => P12 | P14 => P10 end.
Definition fl152_154 (l:Line) := match l with L0 => L27 | L1 => L28 | L2 => L2 | L3 => L29 | L4 => L17 | L5 => L12 | L6 => L30 | L7 => L6 | L8 => L14 | L9 => L19 | L10 => L23 | L11 => L9 | L12 => L31 | L13 => L18 | L14 => L8 | L15 => L3 | L16 => L20 | L17 => L32 | L18 => L24 | L19 => L13 | L20 => L22 | L21 => L26 | L22 => L10 | L23 => L25 | L24 => L11 | L25 => L16 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L7 | L30 => L15 | L31 => L4 | L32 => L5 | L33 => L1 | L34 => L0 end.

(* P154 : S5 S8 S22 S25 S35 S47 S52 ->
   P157 : S5 S9 S19 S29 S32 S46 S52  *)
Definition fp154_157 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P10 | P4 => P8 | P5 => P7 | P6 => P9 | P7 => P14 | P8 => P12 | P9 => P11 | P10 => P13 | P11 => P3 | P12 => P5 | P13 => P6 | P14 => P4 end.
Definition fl154_157 (l:Line) := match l with L0 => L0 | L1 => L8 | L2 => L10 | L3 => L9 | L4 => L11 | L5 => L12 | L6 => L7 | L7 => L18 | L8 => L16 | L9 => L17 | L10 => L14 | L11 => L15 | L12 => L13 | L13 => L6 | L14 => L1 | L15 => L4 | L16 => L2 | L17 => L3 | L18 => L5 | L19 => L25 | L20 => L30 | L21 => L34 | L22 => L19 | L23 => L24 | L24 => L20 | L25 => L32 | L26 => L27 | L27 => L26 | L28 => L31 | L29 => L22 | L30 => L28 | L31 => L23 | L32 => L33 | L33 => L29 | L34 => L21 end.

(* P157 : S5 S9 S19 S29 S32 S46 S52 ->
   P158 : S5 S9 S20 S28 S35 S41 S54  *)
Definition fp157_158 (p:Point) := match p with P0 => P12 | P1 => P7 | P2 => P4 | P3 => P13 | P4 => P2 | P5 => P5 | P6 => P10 | P7 => P1 | P8 => P14 | P9 => P9 | P10 => P6 | P11 => P11 | P12 => P0 | P13 => P3 | P14 => P8 end.
Definition fl157_158 (l:Line) := match l with L0 => L26 | L1 => L16 | L2 => L30 | L3 => L9 | L4 => L33 | L5 => L5 | L6 => L20 | L7 => L13 | L8 => L31 | L9 => L3 | L10 => L10 | L11 => L22 | L12 => L28 | L13 => L7 | L14 => L24 | L15 => L25 | L16 => L1 | L17 => L17 | L18 => L23 | L19 => L32 | L20 => L6 | L21 => L21 | L22 => L11 | L23 => L18 | L24 => L14 | L25 => L15 | L26 => L0 | L27 => L27 | L28 => L12 | L29 => L29 | L30 => L2 | L31 => L8 | L32 => L19 | L33 => L4 | L34 => L34 end.

(* P158 : S5 S9 S20 S28 S35 S41 S54 ->
   P160 : S5 S9 S22 S30 S34 S45 S49  *)
Definition fp158_160 (p:Point) := match p with P0 => P13 | P1 => P9 | P2 => P3 | P3 => P12 | P4 => P2 | P5 => P6 | P6 => P8 | P7 => P1 | P8 => P11 | P9 => P7 | P10 => P5 | P11 => P14 | P12 => P0 | P13 => P4 | P14 => P10 end.
Definition fl158_160 (l:Line) := match l with L0 => L21 | L1 => L16 | L2 => L32 | L3 => L11 | L4 => L28 | L5 => L6 | L6 => L25 | L7 => L18 | L8 => L29 | L9 => L4 | L10 => L10 | L11 => L23 | L12 => L33 | L13 => L12 | L14 => L19 | L15 => L20 | L16 => L1 | L17 => L15 | L18 => L22 | L19 => L30 | L20 => L5 | L21 => L26 | L22 => L9 | L23 => L13 | L24 => L14 | L25 => L17 | L26 => L0 | L27 => L34 | L28 => L7 | L29 => L31 | L30 => L2 | L31 => L8 | L32 => L24 | L33 => L3 | L34 => L27 end.

(* P160 : S5 S9 S22 S30 S34 S45 S49 ->
   P163 : S5 S10 S17 S30 S37 S41 S52  *)
Definition fp160_163 (p:Point) := match p with P0 => P13 | P1 => P3 | P2 => P9 | P3 => P6 | P4 => P8 | P5 => P2 | P6 => P12 | P7 => P14 | P8 => P0 | P9 => P10 | P10 => P4 | P11 => P7 | P12 => P5 | P13 => P11 | P14 => P1 end.
Definition fl160_163 (l:Line) := match l with L0 => L21 | L1 => L32 | L2 => L16 | L3 => L6 | L4 => L25 | L5 => L28 | L6 => L11 | L7 => L20 | L8 => L1 | L9 => L12 | L10 => L19 | L11 => L22 | L12 => L15 | L13 => L23 | L14 => L10 | L15 => L33 | L16 => L29 | L17 => L18 | L18 => L4 | L19 => L7 | L20 => L2 | L21 => L34 | L22 => L31 | L23 => L8 | L24 => L3 | L25 => L24 | L26 => L27 | L27 => L0 | L28 => L14 | L29 => L13 | L30 => L17 | L31 => L9 | L32 => L5 | L33 => L30 | L34 => L26 end.

(* P163 : S5 S10 S17 S30 S37 S41 S52 ->
   P165 : S5 S10 S20 S29 S39 S42 S49  *)
Definition fp163_165 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl163_165 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P165 : S5 S10 S20 S29 S39 S42 S49 ->
   P166 : S5 S10 S21 S28 S32 S47 S51  *)
Definition fp165_166 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P14 | P4 => P12 | P5 => P13 | P6 => P11 | P7 => P7 | P8 => P9 | P9 => P8 | P10 => P10 | P11 => P6 | P12 => P4 | P13 => P5 | P14 => P3 end.
Definition fl165_166 (l:Line) := match l with L0 => L0 | L1 => L9 | L2 => L11 | L3 => L10 | L4 => L8 | L5 => L7 | L6 => L12 | L7 => L5 | L8 => L4 | L9 => L1 | L10 => L3 | L11 => L2 | L12 => L6 | L13 => L13 | L14 => L15 | L15 => L14 | L16 => L17 | L17 => L16 | L18 => L18 | L19 => L19 | L20 => L23 | L21 => L27 | L22 => L31 | L23 => L20 | L24 => L33 | L25 => L30 | L26 => L26 | L27 => L21 | L28 => L28 | L29 => L32 | L30 => L25 | L31 => L22 | L32 => L29 | L33 => L24 | L34 => L34 end.

(* P166 : S5 S10 S21 S28 S32 S47 S51 ->
   P169 : S5 S12 S17 S29 S34 S47 S48  *)
Definition fp166_169 (p:Point) := match p with P0 => P14 | P1 => P8 | P2 => P5 | P3 => P2 | P4 => P11 | P5 => P9 | P6 => P4 | P7 => P10 | P8 => P3 | P9 => P1 | P10 => P12 | P11 => P7 | P12 => P6 | P13 => P0 | P14 => P13 end.
Definition fl166_169 (l:Line) := match l with L0 => L27 | L1 => L14 | L2 => L23 | L3 => L19 | L4 => L9 | L5 => L31 | L6 => L6 | L7 => L24 | L8 => L20 | L9 => L32 | L10 => L8 | L11 => L3 | L12 => L18 | L13 => L30 | L14 => L28 | L15 => L17 | L16 => L2 | L17 => L29 | L18 => L12 | L19 => L16 | L20 => L15 | L21 => L0 | L22 => L13 | L23 => L11 | L24 => L22 | L25 => L5 | L26 => L34 | L27 => L21 | L28 => L4 | L29 => L10 | L30 => L33 | L31 => L25 | L32 => L1 | L33 => L7 | L34 => L26 end.

(* P169 : S5 S12 S17 S29 S34 S47 S48 ->
   P170 : S5 S12 S19 S25 S37 S42 S54  *)
Definition fp169_170 (p:Point) := match p with P0 => P3 | P1 => P9 | P2 => P13 | P3 => P0 | P4 => P4 | P5 => P10 | P6 => P14 | P7 => P7 | P8 => P11 | P9 => P1 | P10 => P5 | P11 => P8 | P12 => P12 | P13 => P2 | P14 => P6 end.
Definition fl169_170 (l:Line) := match l with L0 => L21 | L1 => L1 | L2 => L19 | L3 => L22 | L4 => L12 | L5 => L20 | L6 => L15 | L7 => L23 | L8 => L29 | L9 => L33 | L10 => L10 | L11 => L18 | L12 => L4 | L13 => L28 | L14 => L32 | L15 => L6 | L16 => L16 | L17 => L25 | L18 => L11 | L19 => L2 | L20 => L5 | L21 => L0 | L22 => L3 | L23 => L7 | L24 => L24 | L25 => L17 | L26 => L26 | L27 => L34 | L28 => L13 | L29 => L8 | L30 => L30 | L31 => L31 | L32 => L14 | L33 => L9 | L34 => L27 end.

(* P170 : S5 S12 S19 S25 S37 S42 S54 ->
   P173 : S5 S12 S22 S26 S39 S41 S51  *)
Definition fp170_173 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl170_173 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P173 : S5 S12 S22 S26 S39 S41 S51 ->
   P174 : S5 S15 S17 S26 S32 S45 S54  *)
Definition fp173_174 (p:Point) := match p with P0 => P12 | P1 => P7 | P2 => P4 | P3 => P10 | P4 => P5 | P5 => P2 | P6 => P13 | P7 => P14 | P8 => P1 | P9 => P6 | P10 => P9 | P11 => P3 | P12 => P8 | P13 => P11 | P14 => P0 end.
Definition fl173_174 (l:Line) := match l with L0 => L26 | L1 => L30 | L2 => L16 | L3 => L9 | L4 => L33 | L5 => L20 | L6 => L5 | L7 => L28 | L8 => L10 | L9 => L3 | L10 => L31 | L11 => L22 | L12 => L13 | L13 => L23 | L14 => L1 | L15 => L25 | L16 => L24 | L17 => L17 | L18 => L7 | L19 => L4 | L20 => L8 | L21 => L34 | L22 => L19 | L23 => L2 | L24 => L12 | L25 => L29 | L26 => L27 | L27 => L0 | L28 => L14 | L29 => L15 | L30 => L18 | L31 => L6 | L32 => L11 | L33 => L32 | L34 => L21 end.

(* P174 : S5 S15 S17 S26 S32 S45 S54 ->
   P176 : S5 S15 S20 S25 S34 S46 S51  *)
Definition fp174_176 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P3 | P4 => P4 | P5 => P6 | P6 => P5 | P7 => P12 | P8 => P11 | P9 => P13 | P10 => P14 | P11 => P8 | P12 => P7 | P13 => P9 | P14 => P10 end.
Definition fl174_176 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L5 | L4 => L6 | L5 => L3 | L6 => L4 | L7 => L17 | L8 => L14 | L9 => L13 | L10 => L16 | L11 => L18 | L12 => L15 | L13 => L9 | L14 => L8 | L15 => L12 | L16 => L10 | L17 => L7 | L18 => L11 | L19 => L19 | L20 => L22 | L21 => L21 | L22 => L20 | L23 => L25 | L24 => L24 | L25 => L23 | L26 => L26 | L27 => L34 | L28 => L33 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L28 | L34 => L27 end.

(* P176 : S5 S15 S20 S25 S34 S46 S51 ->
   P179 : S5 S15 S21 S30 S35 S42 S48  *)
Definition fp176_179 (p:Point) := match p with P0 => P9 | P1 => P3 | P2 => P13 | P3 => P2 | P4 => P8 | P5 => P6 | P6 => P12 | P7 => P5 | P8 => P11 | P9 => P1 | P10 => P7 | P11 => P4 | P12 => P14 | P13 => P0 | P14 => P10 end.
Definition fl176_179 (l:Line) := match l with L0 => L21 | L1 => L18 | L2 => L33 | L3 => L29 | L4 => L10 | L5 => L23 | L6 => L4 | L7 => L20 | L8 => L22 | L9 => L19 | L10 => L12 | L11 => L1 | L12 => L15 | L13 => L28 | L14 => L25 | L15 => L16 | L16 => L6 | L17 => L32 | L18 => L11 | L19 => L13 | L20 => L14 | L21 => L0 | L22 => L17 | L23 => L8 | L24 => L24 | L25 => L3 | L26 => L27 | L27 => L34 | L28 => L2 | L29 => L7 | L30 => L31 | L31 => L30 | L32 => L5 | L33 => L9 | L34 => L26 end.

(* P179 : S5 S15 S21 S30 S35 S42 S48 ->
   P181 : S6 S8 S18 S25 S37 S44 S55  *)
Definition fp179_181 (p:Point) := match p with P0 => P12 | P1 => P5 | P2 => P10 | P3 => P6 | P4 => P9 | P5 => P0 | P6 => P11 | P7 => P14 | P8 => P1 | P9 => P8 | P10 => P3 | P11 => P7 | P12 => P4 | P13 => P13 | P14 => P2 end.
Definition fl179_181 (l:Line) := match l with L0 => L30 | L1 => L33 | L2 => L5 | L3 => L9 | L4 => L20 | L5 => L26 | L6 => L16 | L7 => L29 | L8 => L12 | L9 => L17 | L10 => L27 | L11 => L28 | L12 => L2 | L13 => L19 | L14 => L13 | L15 => L34 | L16 => L25 | L17 => L4 | L18 => L8 | L19 => L15 | L20 => L7 | L21 => L32 | L22 => L31 | L23 => L18 | L24 => L10 | L25 => L21 | L26 => L23 | L27 => L0 | L28 => L6 | L29 => L3 | L30 => L1 | L31 => L14 | L32 => L11 | L33 => L24 | L34 => L22 end.

(* P181 : S6 S8 S18 S25 S37 S44 S55 ->
   P183 : S6 S8 S21 S27 S36 S47 S48  *)
Definition fp181_183 (p:Point) := match p with P0 => P11 | P1 => P7 | P2 => P3 | P3 => P14 | P4 => P2 | P5 => P6 | P6 => P10 | P7 => P9 | P8 => P5 | P9 => P1 | P10 => P13 | P11 => P4 | P12 => P8 | P13 => P12 | P14 => P0 end.
Definition fl181_183 (l:Line) := match l with L0 => L22 | L1 => L14 | L2 => L34 | L3 => L29 | L4 => L11 | L5 => L24 | L6 => L5 | L7 => L13 | L8 => L28 | L9 => L3 | L10 => L10 | L11 => L26 | L12 => L31 | L13 => L21 | L14 => L1 | L15 => L19 | L16 => L20 | L17 => L15 | L18 => L12 | L19 => L6 | L20 => L27 | L21 => L9 | L22 => L23 | L23 => L0 | L24 => L17 | L25 => L16 | L26 => L18 | L27 => L2 | L28 => L33 | L29 => L7 | L30 => L32 | L31 => L4 | L32 => L30 | L33 => L8 | L34 => L25 end.

(* P183 : S6 S8 S21 S27 S36 S47 S48 ->
   P184 : S6 S8 S23 S26 S39 S40 S53  *)
Definition fp183_184 (p:Point) := match p with P0 => P11 | P1 => P7 | P2 => P3 | P3 => P2 | P4 => P14 | P5 => P10 | P6 => P6 | P7 => P1 | P8 => P13 | P9 => P9 | P10 => P5 | P11 => P0 | P12 => P12 | P13 => P8 | P14 => P4 end.
Definition fl183_184 (l:Line) := match l with L0 => L22 | L1 => L14 | L2 => L34 | L3 => L11 | L4 => L29 | L5 => L5 | L6 => L24 | L7 => L31 | L8 => L28 | L9 => L26 | L10 => L10 | L11 => L3 | L12 => L13 | L13 => L12 | L14 => L1 | L15 => L15 | L16 => L20 | L17 => L19 | L18 => L21 | L19 => L17 | L20 => L16 | L21 => L18 | L22 => L0 | L23 => L23 | L24 => L6 | L25 => L27 | L26 => L9 | L27 => L25 | L28 => L8 | L29 => L4 | L30 => L30 | L31 => L7 | L32 => L32 | L33 => L33 | L34 => L2 end.

(* P184 : S6 S8 S23 S26 S39 S40 S53 ->
   P187 : S6 S9 S18 S30 S36 S41 S53  *)
Definition fp184_187 (p:Point) := match p with P0 => P2 | P1 => P0 | P2 => P1 | P3 => P13 | P4 => P12 | P5 => P14 | P6 => P11 | P7 => P6 | P8 => P3 | P9 => P5 | P10 => P4 | P11 => P8 | P12 => P9 | P13 => P7 | P14 => P10 end.
Definition fl184_187 (l:Line) := match l with L0 => L0 | L1 => L16 | L2 => L14 | L3 => L15 | L4 => L17 | L5 => L18 | L6 => L13 | L7 => L5 | L8 => L1 | L9 => L4 | L10 => L2 | L11 => L3 | L12 => L6 | L13 => L7 | L14 => L8 | L15 => L11 | L16 => L10 | L17 => L9 | L18 => L12 | L19 => L25 | L20 => L21 | L21 => L28 | L22 => L32 | L23 => L30 | L24 => L20 | L25 => L26 | L26 => L33 | L27 => L19 | L28 => L31 | L29 => L27 | L30 => L23 | L31 => L34 | L32 => L22 | L33 => L29 | L34 => L24 end.

(* P187 : S6 S9 S18 S30 S36 S41 S53 ->
   P189 : S6 S9 S20 S29 S34 S40 S55  *)
Definition fp187_189 (p:Point) := match p with P0 => P5 | P1 => P12 | P2 => P10 | P3 => P9 | P4 => P11 | P5 => P6 | P6 => P0 | P7 => P4 | P8 => P2 | P9 => P7 | P10 => P13 | P11 => P14 | P12 => P8 | P13 => P1 | P14 => P3 end.
Definition fl187_189 (l:Line) := match l with L0 => L30 | L1 => L29 | L2 => L2 | L3 => L17 | L4 => L28 | L5 => L27 | L6 => L12 | L7 => L5 | L8 => L16 | L9 => L20 | L10 => L26 | L11 => L9 | L12 => L33 | L13 => L25 | L14 => L19 | L15 => L4 | L16 => L8 | L17 => L34 | L18 => L13 | L19 => L21 | L20 => L18 | L21 => L10 | L22 => L23 | L23 => L22 | L24 => L14 | L25 => L11 | L26 => L24 | L27 => L15 | L28 => L7 | L29 => L31 | L30 => L32 | L31 => L1 | L32 => L0 | L33 => L3 | L34 => L6 end.

(* P189 : S6 S9 S20 S29 S34 S40 S55 ->
   P190 : S6 S9 S23 S27 S32 S44 S54  *)
Definition fp189_190 (p:Point) := match p with P0 => P5 | P1 => P12 | P2 => P10 | P3 => P9 | P4 => P11 | P5 => P6 | P6 => P0 | P7 => P4 | P8 => P2 | P9 => P7 | P10 => P13 | P11 => P14 | P12 => P8 | P13 => P1 | P14 => P3 end.
Definition fl189_190 (l:Line) := match l with L0 => L30 | L1 => L29 | L2 => L2 | L3 => L17 | L4 => L28 | L5 => L27 | L6 => L12 | L7 => L5 | L8 => L16 | L9 => L20 | L10 => L26 | L11 => L9 | L12 => L33 | L13 => L25 | L14 => L19 | L15 => L4 | L16 => L8 | L17 => L34 | L18 => L13 | L19 => L21 | L20 => L18 | L21 => L10 | L22 => L23 | L23 => L22 | L24 => L14 | L25 => L11 | L26 => L24 | L27 => L15 | L28 => L7 | L29 => L31 | L30 => L32 | L31 => L1 | L32 => L0 | L33 => L3 | L34 => L6 end.

(* P190 : S6 S9 S23 S27 S32 S44 S54 ->
   P193 : S6 S11 S16 S29 S39 S44 S48  *)
Definition fp190_193 (p:Point) := match p with P0 => P12 | P1 => P5 | P2 => P10 | P3 => P14 | P4 => P1 | P5 => P8 | P6 => P3 | P7 => P4 | P8 => P7 | P9 => P2 | P10 => P13 | P11 => P9 | P12 => P6 | P13 => P11 | P14 => P0 end.
Definition fl190_193 (l:Line) := match l with L0 => L30 | L1 => L9 | L2 => L20 | L3 => L26 | L4 => L16 | L5 => L33 | L6 => L5 | L7 => L12 | L8 => L28 | L9 => L2 | L10 => L17 | L11 => L29 | L12 => L27 | L13 => L25 | L14 => L4 | L15 => L19 | L16 => L34 | L17 => L8 | L18 => L13 | L19 => L6 | L20 => L31 | L21 => L14 | L22 => L23 | L23 => L0 | L24 => L10 | L25 => L11 | L26 => L7 | L27 => L3 | L28 => L24 | L29 => L18 | L30 => L32 | L31 => L1 | L32 => L22 | L33 => L15 | L34 => L21 end.

(* P193 : S6 S11 S16 S29 S39 S44 S48 ->
   P194 : S6 S11 S20 S25 S36 S43 S54  *)
Definition fp193_194 (p:Point) := match p with P0 => P9 | P1 => P14 | P2 => P4 | P3 => P8 | P4 => P2 | P5 => P5 | P6 => P11 | P7 => P13 | P8 => P3 | P9 => P0 | P10 => P10 | P11 => P6 | P12 => P12 | P13 => P7 | P14 => P1 end.
Definition fl193_194 (l:Line) := match l with L0 => L23 | L1 => L18 | L2 => L29 | L3 => L21 | L4 => L4 | L5 => L33 | L6 => L10 | L7 => L14 | L8 => L19 | L9 => L9 | L10 => L6 | L11 => L31 | L12 => L27 | L13 => L25 | L14 => L7 | L15 => L24 | L16 => L26 | L17 => L17 | L18 => L1 | L19 => L8 | L20 => L20 | L21 => L3 | L22 => L32 | L23 => L0 | L24 => L15 | L25 => L13 | L26 => L16 | L27 => L12 | L28 => L28 | L29 => L2 | L30 => L30 | L31 => L11 | L32 => L22 | L33 => L5 | L34 => L34 end.

(* P194 : S6 S11 S20 S25 S36 S43 S54 ->
   P197 : S6 S11 S21 S30 S37 S40 S50  *)
Definition fp194_197 (p:Point) := match p with P0 => P14 | P1 => P9 | P2 => P4 | P3 => P12 | P4 => P1 | P5 => P6 | P6 => P7 | P7 => P10 | P8 => P3 | P9 => P0 | P10 => P13 | P11 => P5 | P12 => P8 | P13 => P11 | P14 => P2 end.
Definition fl194_197 (l:Line) := match l with L0 => L23 | L1 => L9 | L2 => L31 | L3 => L19 | L4 => L6 | L5 => L27 | L6 => L14 | L7 => L10 | L8 => L21 | L9 => L18 | L10 => L4 | L11 => L29 | L12 => L33 | L13 => L25 | L14 => L17 | L15 => L26 | L16 => L24 | L17 => L7 | L18 => L1 | L19 => L16 | L20 => L20 | L21 => L5 | L22 => L30 | L23 => L0 | L24 => L12 | L25 => L11 | L26 => L8 | L27 => L15 | L28 => L34 | L29 => L2 | L30 => L32 | L31 => L13 | L32 => L22 | L33 => L3 | L34 => L28 end.

(* P197 : S6 S11 S21 S30 S37 S40 S50 ->
   P198 : S6 S13 S16 S26 S37 S41 S54  *)
Definition fp197_198 (p:Point) := match p with P0 => P8 | P1 => P13 | P2 => P6 | P3 => P14 | P4 => P5 | P5 => P0 | P6 => P7 | P7 => P4 | P8 => P11 | P9 => P10 | P10 => P1 | P11 => P9 | P12 => P2 | P13 => P3 | P14 => P12 end.
Definition fl197_198 (l:Line) := match l with L0 => L32 | L1 => L27 | L2 => L3 | L3 => L24 | L4 => L8 | L5 => L18 | L6 => L20 | L7 => L28 | L8 => L11 | L9 => L16 | L10 => L25 | L11 => L21 | L12 => L6 | L13 => L7 | L14 => L33 | L15 => L31 | L16 => L15 | L17 => L2 | L18 => L34 | L19 => L9 | L20 => L14 | L21 => L19 | L22 => L23 | L23 => L30 | L24 => L29 | L25 => L12 | L26 => L17 | L27 => L5 | L28 => L1 | L29 => L4 | L30 => L0 | L31 => L26 | L32 => L22 | L33 => L13 | L34 => L10 end.

(* P198 : S6 S13 S16 S26 S37 S41 S54 ->
   P200 : S6 S13 S18 S29 S32 S47 S50  *)
Definition fp198_200 (p:Point) := match p with P0 => P3 | P1 => P7 | P2 => P11 | P3 => P4 | P4 => P0 | P5 => P12 | P6 => P8 | P7 => P9 | P8 => P13 | P9 => P1 | P10 => P5 | P11 => P14 | P12 => P10 | P13 => P6 | P14 => P2 end.
Definition fl198_200 (l:Line) := match l with L0 => L22 | L1 => L1 | L2 => L20 | L3 => L21 | L4 => L12 | L5 => L19 | L6 => L15 | L7 => L3 | L8 => L28 | L9 => L13 | L10 => L10 | L11 => L31 | L12 => L26 | L13 => L29 | L14 => L14 | L15 => L24 | L16 => L34 | L17 => L5 | L18 => L11 | L19 => L17 | L20 => L25 | L21 => L7 | L22 => L23 | L23 => L0 | L24 => L6 | L25 => L2 | L26 => L4 | L27 => L16 | L28 => L33 | L29 => L9 | L30 => L30 | L31 => L18 | L32 => L32 | L33 => L8 | L34 => L27 end.

(* P200 : S6 S13 S18 S29 S32 S47 S50 ->
   P203 : S6 S13 S23 S30 S34 S43 S48  *)
Definition fp200_203 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P9 | P8 => P10 | P9 => P7 | P10 => P8 | P11 => P14 | P12 => P13 | P13 => P12 | P14 => P11 end.
Definition fl200_203 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L8 | L9 => L11 | L10 => L10 | L11 => L9 | L12 => L7 | L13 => L18 | L14 => L14 | L15 => L17 | L16 => L16 | L17 => L15 | L18 => L13 | L19 => L24 | L20 => L25 | L21 => L26 | L22 => L23 | L23 => L22 | L24 => L19 | L25 => L20 | L26 => L21 | L27 => L34 | L28 => L33 | L29 => L31 | L30 => L32 | L31 => L29 | L32 => L30 | L33 => L28 | L34 => L27 end.

(* P203 : S6 S13 S23 S30 S34 S43 S48 ->
   P204 : S6 S14 S16 S25 S34 S47 S53  *)
Definition fp203_204 (p:Point) := match p with P0 => P14 | P1 => P9 | P2 => P4 | P3 => P8 | P4 => P5 | P5 => P2 | P6 => P11 | P7 => P6 | P8 => P7 | P9 => P12 | P10 => P1 | P11 => P13 | P12 => P0 | P13 => P3 | P14 => P10 end.
Definition fl203_204 (l:Line) := match l with L0 => L23 | L1 => L27 | L2 => L14 | L3 => L31 | L4 => L9 | L5 => L6 | L6 => L19 | L7 => L29 | L8 => L10 | L9 => L4 | L10 => L33 | L11 => L21 | L12 => L18 | L13 => L7 | L14 => L25 | L15 => L24 | L16 => L1 | L17 => L17 | L18 => L26 | L19 => L8 | L20 => L3 | L21 => L20 | L22 => L32 | L23 => L30 | L24 => L28 | L25 => L12 | L26 => L2 | L27 => L13 | L28 => L15 | L29 => L16 | L30 => L0 | L31 => L34 | L32 => L22 | L33 => L5 | L34 => L11 end.

(* P204 : S6 S14 S16 S25 S34 S47 S53 ->
   P207 : S6 S14 S20 S27 S39 S41 S50  *)
Definition fp204_207 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P11 | P4 => P13 | P5 => P14 | P6 => P12 | P7 => P3 | P8 => P5 | P9 => P6 | P10 => P4 | P11 => P7 | P12 => P9 | P13 => P10 | P14 => P8 end.
Definition fl204_207 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L12 | L4 => L7 | L5 => L10 | L6 => L8 | L7 => L16 | L8 => L17 | L9 => L18 | L10 => L15 | L11 => L13 | L12 => L14 | L13 => L1 | L14 => L3 | L15 => L5 | L16 => L4 | L17 => L6 | L18 => L2 | L19 => L24 | L20 => L29 | L21 => L34 | L22 => L22 | L23 => L32 | L24 => L28 | L25 => L25 | L26 => L21 | L27 => L27 | L28 => L19 | L29 => L31 | L30 => L23 | L31 => L20 | L32 => L30 | L33 => L33 | L34 => L26 end.

(* P207 : S6 S14 S20 S27 S39 S41 S50 ->
   P208 : S6 S14 S21 S26 S32 S43 S55  *)
Definition fp207_208 (p:Point) := match p with P0 => P1 | P1 => P0 | P2 => P2 | P3 => P11 | P4 => P13 | P5 => P12 | P6 => P14 | P7 => P7 | P8 => P9 | P9 => P8 | P10 => P10 | P11 => P3 | P12 => P5 | P13 => P4 | P14 => P6 end.
Definition fl207_208 (l:Line) := match l with L0 => L0 | L1 => L11 | L2 => L9 | L3 => L10 | L4 => L8 | L5 => L12 | L6 => L7 | L7 => L6 | L8 => L4 | L9 => L2 | L10 => L3 | L11 => L1 | L12 => L5 | L13 => L13 | L14 => L15 | L15 => L14 | L16 => L17 | L17 => L16 | L18 => L18 | L19 => L34 | L20 => L29 | L21 => L24 | L22 => L22 | L23 => L32 | L24 => L21 | L25 => L25 | L26 => L28 | L27 => L33 | L28 => L26 | L29 => L20 | L30 => L30 | L31 => L31 | L32 => L23 | L33 => L27 | L34 => L19 end.

(* P208 : S6 S14 S21 S26 S32 S43 S55 ->
   P210 : S7 S9 S18 S28 S32 S45 S55  *)
Definition fp208_210 (p:Point) := match p with P0 => P0 | P1 => P2 | P2 => P1 | P3 => P4 | P4 => P3 | P5 => P5 | P6 => P6 | P7 => P10 | P8 => P9 | P9 => P7 | P10 => P8 | P11 => P13 | P12 => P14 | P13 => P12 | P14 => P11 end.
Definition fl208_210 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L15 | L8 => L18 | L9 => L14 | L10 => L13 | L11 => L16 | L12 => L17 | L13 => L8 | L14 => L11 | L15 => L7 | L16 => L9 | L17 => L12 | L18 => L10 | L19 => L24 | L20 => L23 | L21 => L26 | L22 => L25 | L23 => L22 | L24 => L21 | L25 => L20 | L26 => L19 | L27 => L29 | L28 => L30 | L29 => L28 | L30 => L27 | L31 => L34 | L32 => L33 | L33 => L31 | L34 => L32 end.

(* P210 : S7 S9 S18 S28 S32 S45 S55 ->
   P213 : S7 S9 S22 S27 S38 S41 S52  *)
Definition fp210_213 (p:Point) := match p with P0 => P10 | P1 => P13 | P2 => P4 | P3 => P8 | P4 => P1 | P5 => P6 | P6 => P11 | P7 => P5 | P8 => P12 | P9 => P7 | P10 => P2 | P11 => P14 | P12 => P3 | P13 => P0 | P14 => P9 end.
Definition fl210_213 (l:Line) := match l with L0 => L25 | L1 => L8 | L2 => L34 | L3 => L30 | L4 => L13 | L5 => L19 | L6 => L4 | L7 => L11 | L8 => L16 | L9 => L21 | L10 => L28 | L11 => L6 | L12 => L32 | L13 => L17 | L14 => L23 | L15 => L24 | L16 => L1 | L17 => L7 | L18 => L26 | L19 => L18 | L20 => L20 | L21 => L3 | L22 => L27 | L23 => L10 | L24 => L9 | L25 => L0 | L26 => L12 | L27 => L33 | L28 => L2 | L29 => L31 | L30 => L15 | L31 => L29 | L32 => L5 | L33 => L22 | L34 => L14 end.

(* P213 : S7 S9 S22 S27 S38 S41 S52 ->
   P214 : S7 S9 S23 S24 S34 S46 S53  *)
Definition fp213_214 (p:Point) := match p with P0 => P10 | P1 => P4 | P2 => P13 | P3 => P8 | P4 => P1 | P5 => P11 | P6 => P6 | P7 => P14 | P8 => P3 | P9 => P9 | P10 => P0 | P11 => P5 | P12 => P12 | P13 => P2 | P14 => P7 end.
Definition fl213_214 (l:Line) := match l with L0 => L25 | L1 => L8 | L2 => L34 | L3 => L19 | L4 => L4 | L5 => L30 | L6 => L13 | L7 => L7 | L8 => L1 | L9 => L26 | L10 => L23 | L11 => L17 | L12 => L24 | L13 => L6 | L14 => L28 | L15 => L32 | L16 => L16 | L17 => L11 | L18 => L21 | L19 => L3 | L20 => L20 | L21 => L18 | L22 => L27 | L23 => L10 | L24 => L12 | L25 => L0 | L26 => L9 | L27 => L22 | L28 => L14 | L29 => L29 | L30 => L5 | L31 => L31 | L32 => L15 | L33 => L33 | L34 => L2 end.

(* P214 : S7 S9 S23 S24 S34 S46 S53 ->
   P216 : S7 S10 S16 S28 S39 S41 S53  *)
Definition fp214_216 (p:Point) := match p with P0 => P12 | P1 => P6 | P2 => P9 | P3 => P1 | P4 => P14 | P5 => P4 | P6 => P7 | P7 => P2 | P8 => P13 | P9 => P3 | P10 => P8 | P11 => P0 | P12 => P11 | P13 => P5 | P14 => P10 end.
Definition fl214_216 (l:Line) := match l with L0 => L33 | L1 => L9 | L2 => L26 | L3 => L16 | L4 => L20 | L5 => L5 | L6 => L30 | L7 => L31 | L8 => L32 | L9 => L34 | L10 => L15 | L11 => L2 | L12 => L7 | L13 => L18 | L14 => L4 | L15 => L10 | L16 => L29 | L17 => L23 | L18 => L21 | L19 => L8 | L20 => L11 | L21 => L12 | L22 => L0 | L23 => L19 | L24 => L6 | L25 => L27 | L26 => L14 | L27 => L25 | L28 => L17 | L29 => L1 | L30 => L24 | L31 => L13 | L32 => L28 | L33 => L22 | L34 => L3 end.

(* P216 : S7 S10 S16 S28 S39 S41 S53 ->
   P218 : S7 S10 S21 S24 S37 S42 S55  *)
Definition fp216_218 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P4 | P4 => P3 | P5 => P6 | P6 => P5 | P7 => P10 | P8 => P9 | P9 => P8 | P10 => P7 | P11 => P13 | P12 => P14 | P13 => P11 | P14 => P12 end.
Definition fl216_218 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L4 | L4 => L3 | L5 => L6 | L6 => L5 | L7 => L12 | L8 => L10 | L9 => L9 | L10 => L8 | L11 => L11 | L12 => L7 | L13 => L13 | L14 => L16 | L15 => L17 | L16 => L14 | L17 => L15 | L18 => L18 | L19 => L26 | L20 => L23 | L21 => L24 | L22 => L25 | L23 => L20 | L24 => L21 | L25 => L22 | L26 => L19 | L27 => L33 | L28 => L34 | L29 => L32 | L30 => L31 | L31 => L30 | L32 => L29 | L33 => L27 | L34 => L28 end.

(* P218 : S7 S10 S21 S24 S37 S42 S55 ->
   P221 : S7 S10 S23 S31 S32 S43 S52  *)
Definition fp218_221 (p:Point) := match p with P0 => P4 | P1 => P13 | P2 => P10 | P3 => P0 | P4 => P3 | P5 => P14 | P6 => P9 | P7 => P2 | P8 => P5 | P9 => P12 | P10 => P7 | P11 => P1 | P12 => P6 | P13 => P11 | P14 => P8 end.
Definition fl218_221 (l:Line) := match l with L0 => L25 | L1 => L1 | L2 => L23 | L3 => L17 | L4 => L26 | L5 => L7 | L6 => L24 | L7 => L21 | L8 => L28 | L9 => L32 | L10 => L16 | L11 => L11 | L12 => L6 | L13 => L13 | L14 => L8 | L15 => L4 | L16 => L34 | L17 => L19 | L18 => L30 | L19 => L3 | L20 => L2 | L21 => L5 | L22 => L0 | L23 => L20 | L24 => L12 | L25 => L22 | L26 => L15 | L27 => L27 | L28 => L14 | L29 => L9 | L30 => L31 | L31 => L18 | L32 => L29 | L33 => L33 | L34 => L10 end.

(* P221 : S7 S10 S23 S31 S32 S43 S52 ->
   P222 : S7 S11 S16 S25 S37 S46 S52  *)
Definition fp221_222 (p:Point) := match p with P0 => P12 | P1 => P6 | P2 => P9 | P3 => P1 | P4 => P14 | P5 => P4 | P6 => P7 | P7 => P2 | P8 => P13 | P9 => P3 | P10 => P8 | P11 => P0 | P12 => P11 | P13 => P5 | P14 => P10 end.
Definition fl221_222 (l:Line) := match l with L0 => L33 | L1 => L9 | L2 => L26 | L3 => L16 | L4 => L20 | L5 => L5 | L6 => L30 | L7 => L31 | L8 => L32 | L9 => L34 | L10 => L15 | L11 => L2 | L12 => L7 | L13 => L18 | L14 => L4 | L15 => L10 | L16 => L29 | L17 => L23 | L18 => L21 | L19 => L8 | L20 => L11 | L21 => L12 | L22 => L0 | L23 => L19 | L24 => L6 | L25 => L27 | L26 => L14 | L27 => L25 | L28 => L17 | L29 => L1 | L30 => L24 | L31 => L13 | L32 => L28 | L33 => L22 | L34 => L3 end.

(* P222 : S7 S11 S16 S25 S37 S46 S52 ->
   P225 : S7 S11 S21 S28 S38 S43 S48  *)
Definition fp222_225 (p:Point) := match p with P0 => P6 | P1 => P12 | P2 => P9 | P3 => P11 | P4 => P10 | P5 => P0 | P6 => P5 | P7 => P3 | P8 => P2 | P9 => P8 | P10 => P13 | P11 => P7 | P12 => P14 | P13 => P4 | P14 => P1 end.
Definition fl222_225 (l:Line) := match l with L0 => L33 | L1 => L34 | L2 => L2 | L3 => L15 | L4 => L32 | L5 => L31 | L6 => L7 | L7 => L30 | L8 => L16 | L9 => L9 | L10 => L20 | L11 => L26 | L12 => L5 | L13 => L21 | L14 => L10 | L15 => L29 | L16 => L23 | L17 => L4 | L18 => L18 | L19 => L11 | L20 => L14 | L21 => L24 | L22 => L22 | L23 => L8 | L24 => L13 | L25 => L25 | L26 => L19 | L27 => L0 | L28 => L1 | L29 => L3 | L30 => L6 | L31 => L12 | L32 => L17 | L33 => L27 | L34 => L28 end.

(* P225 : S7 S11 S21 S28 S38 S43 S48 ->
   P226 : S7 S11 S22 S24 S39 S45 S50  *)
Definition fp225_226 (p:Point) := match p with P0 => P6 | P1 => P9 | P2 => P12 | P3 => P10 | P4 => P11 | P5 => P0 | P6 => P5 | P7 => P4 | P8 => P1 | P9 => P14 | P10 => P7 | P11 => P13 | P12 => P8 | P13 => P3 | P14 => P2 end.
Definition fl225_226 (l:Line) := match l with L0 => L33 | L1 => L34 | L2 => L2 | L3 => L7 | L4 => L31 | L5 => L32 | L6 => L15 | L7 => L29 | L8 => L10 | L9 => L18 | L10 => L23 | L11 => L21 | L12 => L4 | L13 => L26 | L14 => L16 | L15 => L30 | L16 => L20 | L17 => L5 | L18 => L9 | L19 => L13 | L20 => L8 | L21 => L19 | L22 => L25 | L23 => L14 | L24 => L11 | L25 => L22 | L26 => L24 | L27 => L0 | L28 => L1 | L29 => L6 | L30 => L3 | L31 => L17 | L32 => L12 | L33 => L27 | L34 => L28 end.

(* P226 : S7 S11 S22 S24 S39 S45 S50 ->
   P229 : S7 S12 S18 S31 S37 S41 S50  *)
Definition fp226_229 (p:Point) := match p with P0 => P14 | P1 => P8 | P2 => P5 | P3 => P2 | P4 => P11 | P5 => P9 | P6 => P4 | P7 => P1 | P8 => P12 | P9 => P10 | P10 => P3 | P11 => P0 | P12 => P13 | P13 => P7 | P14 => P6 end.
Definition fl226_229 (l:Line) := match l with L0 => L27 | L1 => L14 | L2 => L23 | L3 => L9 | L4 => L19 | L5 => L6 | L6 => L31 | L7 => L24 | L8 => L20 | L9 => L32 | L10 => L8 | L11 => L3 | L12 => L18 | L13 => L12 | L14 => L2 | L15 => L17 | L16 => L28 | L17 => L29 | L18 => L30 | L19 => L15 | L20 => L16 | L21 => L13 | L22 => L0 | L23 => L34 | L24 => L5 | L25 => L22 | L26 => L11 | L27 => L33 | L28 => L10 | L29 => L4 | L30 => L21 | L31 => L7 | L32 => L26 | L33 => L25 | L34 => L1 end.

(* P229 : S7 S12 S18 S31 S37 S41 S50 ->
   P230 : S7 S12 S22 S25 S34 S43 S55  *)
Definition fp229_230 (p:Point) := match p with P0 => P2 | P1 => P1 | P2 => P0 | P3 => P11 | P4 => P14 | P5 => P13 | P6 => P12 | P7 => P7 | P8 => P10 | P9 => P9 | P10 => P8 | P11 => P3 | P12 => P6 | P13 => P5 | P14 => P4 end.
Definition fl229_230 (l:Line) := match l with L0 => L0 | L1 => L14 | L2 => L16 | L3 => L13 | L4 => L18 | L5 => L15 | L6 => L17 | L7 => L9 | L8 => L8 | L9 => L7 | L10 => L10 | L11 => L12 | L12 => L11 | L13 => L3 | L14 => L1 | L15 => L5 | L16 => L2 | L17 => L6 | L18 => L4 | L19 => L24 | L20 => L34 | L21 => L29 | L22 => L22 | L23 => L23 | L24 => L19 | L25 => L27 | L26 => L31 | L27 => L25 | L28 => L28 | L29 => L21 | L30 => L32 | L31 => L26 | L32 => L30 | L33 => L33 | L34 => L20 end.

(* P230 : S7 S12 S22 S25 S34 S43 S55 ->
   P232 : S7 S12 S23 S27 S39 S42 S48  *)
Definition fp230_232 (p:Point) := match p with P0 => P1 | P1 => P2 | P2 => P0 | P3 => P7 | P4 => P9 | P5 => P10 | P6 => P8 | P7 => P11 | P8 => P13 | P9 => P14 | P10 => P12 | P11 => P3 | P12 => P5 | P13 => P6 | P14 => P4 end.
Definition fl230_232 (l:Line) := match l with L0 => L0 | L1 => L10 | L2 => L8 | L3 => L11 | L4 => L9 | L5 => L12 | L6 => L7 | L7 => L18 | L8 => L16 | L9 => L17 | L10 => L14 | L11 => L15 | L12 => L13 | L13 => L5 | L14 => L1 | L15 => L3 | L16 => L2 | L17 => L4 | L18 => L6 | L19 => L26 | L20 => L28 | L21 => L31 | L22 => L22 | L23 => L23 | L24 => L21 | L25 => L33 | L26 => L29 | L27 => L25 | L28 => L34 | L29 => L19 | L30 => L30 | L31 => L24 | L32 => L32 | L33 => L27 | L34 => L20 end.

(* P232 : S7 S12 S23 S27 S39 S42 S48 ->
   P235 : S7 S15 S16 S31 S34 S45 S48  *)
Definition fp232_235 (p:Point) := match p with P0 => P9 | P1 => P6 | P2 => P12 | P3 => P8 | P4 => P2 | P5 => P13 | P6 => P3 | P7 => P14 | P8 => P4 | P9 => P7 | P10 => P1 | P11 => P5 | P12 => P11 | P13 => P0 | P14 => P10 end.
Definition fl232_235 (l:Line) := match l with L0 => L33 | L1 => L18 | L2 => L21 | L3 => L23 | L4 => L10 | L5 => L29 | L6 => L4 | L7 => L15 | L8 => L7 | L9 => L34 | L10 => L31 | L11 => L2 | L12 => L32 | L13 => L9 | L14 => L30 | L15 => L20 | L16 => L5 | L17 => L16 | L18 => L26 | L19 => L8 | L20 => L24 | L21 => L3 | L22 => L27 | L23 => L13 | L24 => L17 | L25 => L0 | L26 => L14 | L27 => L25 | L28 => L6 | L29 => L28 | L30 => L11 | L31 => L19 | L32 => L1 | L33 => L22 | L34 => L12 end.

(* P235 : S7 S15 S16 S31 S34 S45 S48 ->
   P236 : S7 S15 S18 S25 S38 S42 S53  *)
Definition fp235_236 (p:Point) := match p with P0 => P11 | P1 => P3 | P2 => P7 | P3 => P1 | P4 => P13 | P5 => P5 | P6 => P9 | P7 => P2 | P8 => P14 | P9 => P6 | P10 => P10 | P11 => P0 | P12 => P12 | P13 => P4 | P14 => P8 end.
Definition fl235_236 (l:Line) := match l with L0 => L22 | L1 => L11 | L2 => L29 | L3 => L14 | L4 => L34 | L5 => L5 | L6 => L24 | L7 => L21 | L8 => L19 | L9 => L20 | L10 => L15 | L11 => L1 | L12 => L12 | L13 => L13 | L14 => L3 | L15 => L10 | L16 => L26 | L17 => L28 | L18 => L31 | L19 => L8 | L20 => L9 | L21 => L7 | L22 => L0 | L23 => L32 | L24 => L6 | L25 => L25 | L26 => L16 | L27 => L27 | L28 => L17 | L29 => L2 | L30 => L30 | L31 => L18 | L32 => L23 | L33 => L33 | L34 => L4 end.

(* P236 : S7 S15 S18 S25 S38 S42 S53 ->
   P238 : S7 S15 S21 S27 S32 S46 S50  *)
Definition fp236_238 (p:Point) := match p with P0 => P13 | P1 => P4 | P2 => P10 | P3 => P1 | P4 => P11 | P5 => P6 | P6 => P8 | P7 => P2 | P8 => P12 | P9 => P5 | P10 => P7 | P11 => P0 | P12 => P14 | P13 => P3 | P14 => P9 end.
Definition fl236_238 (l:Line) := match l with L0 => L25 | L1 => L11 | L2 => L32 | L3 => L16 | L4 => L28 | L5 => L6 | L6 => L21 | L7 => L24 | L8 => L26 | L9 => L23 | L10 => L17 | L11 => L1 | L12 => L7 | L13 => L13 | L14 => L4 | L15 => L8 | L16 => L19 | L17 => L34 | L18 => L30 | L19 => L10 | L20 => L9 | L21 => L12 | L22 => L0 | L23 => L29 | L24 => L5 | L25 => L22 | L26 => L14 | L27 => L33 | L28 => L15 | L29 => L2 | L30 => L31 | L31 => L18 | L32 => L20 | L33 => L27 | L34 => L3 end.

(* P238 : S7 S15 S21 S27 S32 S46 S50 ->
   P1 : S0 S9 S19 S28 S38 S40 S53  *)
Definition fp238_1 (p:Point) := match p with P0 => P0 | P1 => P1 | P2 => P2 | P3 => P3 | P4 => P4 | P5 => P5 | P6 => P6 | P7 => P14 | P8 => P13 | P9 => P12 | P10 => P11 | P11 => P10 | P12 => P9 | P13 => P8 | P14 => P7 end.
Definition fl238_1 (l:Line) := match l with L0 => L0 | L1 => L1 | L2 => L2 | L3 => L6 | L4 => L5 | L5 => L4 | L6 => L3 | L7 => L7 | L8 => L11 | L9 => L10 | L10 => L9 | L11 => L8 | L12 => L12 | L13 => L14 | L14 => L13 | L15 => L15 | L16 => L18 | L17 => L17 | L18 => L16 | L19 => L22 | L20 => L21 | L21 => L20 | L22 => L19 | L23 => L26 | L24 => L25 | L25 => L24 | L26 => L23 | L27 => L28 | L28 => L27 | L29 => L30 | L30 => L29 | L31 => L31 | L32 => L32 | L33 => L33 | L34 => L34 end.

(*Check (map fl238_1).*)

Import ListNotations.

Fixpoint insert t s :=
  match s with
  | [] => [t]
  | x::xs => if leL t x then t::(x::xs) else x::(insert t xs)
  end.

Functional Scheme insert_ind := Induction for insert Sort Prop.

Fixpoint sort s :=
  match s with
  | [] => []
  | x::xs => insert x (sort xs)
  end.
Functional Scheme sort_ind := Induction for sort Sort Prop.

(* Eval compute in sort [L5;L1;L8;L2]. *)

Fixpoint sorted s :=
  match s with
  | [] => true
  | x::[] => true
  | x::(y::xs) as z => leL x y && (sorted (z))
  end.

Functional Scheme sorted_ind := Induction for sorted Sort Prop.

Lemma leL_flip : forall x y, leL x y = false -> leL y x = true.
Proof.
  unfold leL;
  destruct x; destruct y; simpl; try solve [intros; discriminate | reflexivity].
Qed.

Lemma leL_eq : forall x y, leL x y -> leL y x -> x=y.
Proof.
  intros x y; destruct x; destruct y; solve [reflexivity | discriminate].
Qed.

Lemma leL_insert : forall x y xs, leL y x = false -> insert x (y :: xs)= x::y::xs.
Proof.
  intros.
  assert (leL x y) by (apply leL_flip; assumption).
  revert x y H H0.
  induction xs.
  simpl.
  intros.
  case_eq (leL x y).
  trivial.
  rewrite H0.
  intros; discriminate.
  intros.
  unfold insert.
  case_eq (leL x y).
  trivial.
  rewrite H0.
  intros; discriminate.
Qed.

Lemma sorted_sort : forall s, sorted s -> sort s = s.
Proof.
  intros; functional induction (sorted s) using sorted_ind.
  simpl; reflexivity.
  simpl; reflexivity.
  replace (sort (x::y::_x)) with (insert x (sort (y::_x))) by reflexivity.
  revert H; rewrite and_bool; intros H.
  destruct H as [HA HB].
  rewrite IHb.
  assumption.
  unfold insert.
  case_eq (leL x y).
  reflexivity.
  rewrite HA.
  intros; discriminate.
Qed.

Lemma sorted_insert : forall x l, sorted l -> sorted (insert x l).
Proof.
  intros; functional induction (sorted l) using sorted_ind.
  reflexivity.
  simpl; case_eq (leL x x0); intros.
  simpl.
  apply and_bool; split; solve [assumption|reflexivity].
  simpl.
  apply and_bool; split.
  apply leL_flip; assumption.
  reflexivity.

  simpl.
  case_eq (leL x x0); intros.
  simpl sorted.
  apply and_bool.
  split; assumption.
  case_eq (leL x y); intros.
  simpl.
  apply and_bool.
  split.
  apply leL_flip; assumption.
  apply and_bool.
  split.
  assumption.
  apply and_bool_lr in H.
  tauto.

  apply and_bool_lr in H.
  destruct H as [Ha Hb].
  generalize (IHb Hb); intros Hs.

  replace  (x0 :: y :: insert x _x) with (x0 ::(insert x (y::_x))).

  simpl insert.
  rewrite H1.
  simpl in Hs.
  rewrite H1 in Hs.
  change (leL x0 y && sorted (y::insert x _x)).
  apply and_bool.
  split.
  assumption.
  assumption.
  simpl; rewrite H1; reflexivity.
Qed.

Lemma sorted_sort_2 : forall l, sorted (sort l).
Proof.
intros; functional induction (sort l) using sort_ind.
trivial.
apply sorted_insert.
assumption.
Qed.

Lemma insert_x_y_l : forall l x y, sorted l -> insert x (insert y l) = insert y (insert x l).
Proof.
  intros l; induction l.
  intros; simpl.
  case_eq (leL x y); intros H1.
  case_eq (leL y x); intros H2.
  assert (Heq:x=y) by (apply leL_eq; assumption).
  subst; reflexivity.
  reflexivity.
  case_eq (leL y x); intros H2.
  reflexivity.
  specialize (leL_flip _ _ H1) as H1'.
  specialize (leL_flip _ _ H2) as H2'.
  assert (Heq:x=y) by (apply leL_eq; assumption).
  subst; reflexivity.
  intros.
  assert (Hs:(sorted l)).
  inversion H.
  destruct l.
  trivial.
  generalize (and_bool_lr _ _ H1); solve [intuition].
  simpl (insert y (a :: l)).
  case_eq (leL y a); intros Hya.
  simpl ((insert x (a :: l))).

  case_eq (leL x a); intros Hxa.
  simpl.
  rewrite Hya Hxa.
  case_eq (leL x y); case_eq (leL y x); intros.
  assert (Hxy:x=y) by (apply leL_eq; assumption).
  rewrite Hxy; reflexivity.
  reflexivity.
  reflexivity.
  assert (Hxy:x=y) by (destruct x; destruct y; solve [reflexivity | discriminate]).
  rewrite Hxy; reflexivity.

  simpl.
  rewrite Hya Hxa.
  case_eq (leL x y); intros.
  assert (Hf:False).
  apply PeanoNat.Nat.leb_le in Hya; apply PeanoNat.Nat.leb_nle in Hxa; apply PeanoNat.Nat.leb_le in H0; lia.
  destruct Hf.
  reflexivity.

  simpl.
  case_eq (leL x a); intros Hxa.
  simpl.
  rewrite Hya.
  case_eq (leL y x); intros.
  assert (Hf:False).
  apply PeanoNat.Nat.leb_le in Hxa; apply PeanoNat.Nat.leb_nle in Hya; apply PeanoNat.Nat.leb_le in H0; lia.
  destruct Hf.
  reflexivity.

  rewrite IHl.
  assumption.
  simpl.
  rewrite Hya.
  reflexivity.
Qed.

Lemma sort_insert_comm : forall x l, sort (insert x l) = insert x (sort l).
Proof.
  intros x l; revert x; induction l.
  simpl; reflexivity.
  intros x; simpl.
  case_eq (leL x a); intros.
  rewrite <- IHl.
  simpl.
  rewrite IHl.
  reflexivity.
  rewrite <- IHl.
  simpl.
  rewrite IHl.
  rewrite IHl.
  rewrite insert_x_y_l.
  apply sorted_sort_2.
  reflexivity.
Qed.

Lemma sort_map : forall f a x, sorted x -> sort (map f (insert a x)) = insert (f a) (sort (map f x)).
Proof.
  intros f a x; revert f a.
  induction x.
  simpl;reflexivity.
  intros.
  simpl.
  rewrite <- IHx.
  rewrite <- (sort_insert_comm (f a0)).
  case_eq (leL a0 a); intros.
  simpl.
  rewrite (sort_insert_comm (f a0)).
  rewrite <- IHx.
  reflexivity.
  inversion H.
  destruct x.
  assumption.
  apply and_bool_lr in H2; tauto.

  simpl.
  rewrite sort_insert_comm.
  rewrite  IHx.
  inversion H.
  destruct x.
  assumption.
  apply and_bool_lr in H2; tauto.
  rewrite IHx.
  inversion H.
  destruct x.
  assumption.
  apply and_bool_lr in H2; tauto.
  rewrite insert_x_y_l.
  apply sorted_sort_2.
  reflexivity.
  inversion H.
  destruct x.
  assumption.
  apply and_bool_lr in H1; tauto.
Qed.

Lemma sort_sort_map : forall f x,  (sort (sort (map f x))) = (sort (map f (sort x))).
Proof.
  intros.
  induction x.
  simpl; reflexivity.
  simpl.
  rewrite sort_insert_comm.
  rewrite IHx.
  rewrite sort_map.
  apply sorted_sort_2.
  reflexivity.
Qed.

Lemma sort_insert_sort : forall x a f, sort (map f (insert a (sort x))) = sort (insert (f a) (map f (sort x))).
Proof.
  intros.
  rewrite sort_insert_comm.
  rewrite sort_map.
  apply sorted_sort_2.
  reflexivity.
Qed.

Lemma sort_map_sort : forall x (f :Line->Line), (sort (map f (sort x))=sort (map f x)).
Proof.
  induction x.
  simpl;reflexivity.
  intros.
  rewrite sort_insert_sort.
  simpl map.
  rewrite sort_insert_comm.
  simpl.
  rewrite IHx.
  reflexivity.
Qed.

Lemma sorted_spreads : forall s:(list Line), In s spreads -> sorted s.
Proof.
intros s H.
repeat match goal with K:In _ _ |- _ => inversion_clear K;  [subst; reflexivity| idtac] end.
destruct (in_nil H).
Qed.

Lemma sorted_spreads' : forall s:(list Line), In s spreads -> sort s=s.
Proof.
intros s H.
repeat match goal with K:In _ _ |- _ => inversion_clear K;  [subst; reflexivity| idtac] end.
destruct (in_nil H).
Qed.

Definition are_isomorphic (p1:list (list Line)) (p2:list (list Line)) : Prop :=
  exists fp, exists fl,
      is_collineation fp fl /\
      forall s:(list Line) (* spread *), In s spreads -> In s p1 -> In (sort (map fl s)) spreads /\ In (sort (map fl s)) p2.

Ltac is_col2 :=
  intros;
  repeat (match goal with H:In _ _ |- _ =>
                          first [elim (in_nil H) | inversion_clear H; [solve [subst; simpl; intuition] | idtac]] end).

Lemma are_iso_P0_P3 : are_isomorphic PA0 PA3.
Proof.
  exists fp0_3.
  exists fl0_3.
  split; [is_col | is_col2].
Qed.

Lemma are_iso_P238_P1 : are_isomorphic PA238 PA1.
Proof.
  exists fp238_1.
  exists fl238_1.
  split; [is_col | is_col2].
Qed.

Lemma n120_decomp : forall n:nat, n < 120 <->
                        n = 0 \/ n = 1 \/ n = 2 \/ n = 3 \/ n = 4 \/ n = 5 \/ n = 6 \/ n = 7 \/ n  = 8 \/ n = 9 \/
                        n = 10 \/ n = 11 \/ n = 12 \/ n = 13 \/ n = 14 \/ n = 15 \/ n = 16 \/ n = 17 \/ n  = 18 \/ n = 19 \/
                        n = 20 \/ n = 21 \/ n = 22 \/ n = 23 \/ n = 24 \/ n = 25 \/ n = 26 \/ n = 27 \/ n  = 28 \/ n = 29 \/
                        n = 30 \/ n = 31 \/ n = 32 \/ n = 33 \/ n = 34 \/ n = 35 \/ n = 36 \/ n = 37 \/ n  = 38 \/ n = 39 \/
                        n = 40 \/ n = 41 \/ n = 42 \/ n = 43 \/ n = 44 \/ n = 45 \/ n = 46 \/ n = 47 \/ n  = 48 \/ n = 49 \/
                        n = 50 \/ n = 51 \/ n = 52 \/ n = 53 \/ n = 54 \/ n = 55 \/ n = 56 \/ n = 57 \/ n  = 58 \/ n = 59 \/
                        n = 60 \/ n = 61 \/ n = 62 \/ n = 63 \/ n = 64 \/ n = 65 \/ n = 66 \/ n = 67 \/ n  = 68 \/ n = 69 \/
                        n = 70 \/ n = 71 \/ n = 72 \/ n = 73 \/ n = 74 \/ n = 75 \/ n = 76 \/ n = 77 \/ n  = 78 \/ n = 79 \/
                        n = 80 \/ n = 81 \/ n = 82 \/ n = 83 \/ n = 84 \/ n = 85 \/ n = 86 \/ n = 87 \/ n  = 88 \/ n = 89 \/
                        n = 90 \/ n = 91 \/ n = 92 \/ n = 93 \/ n = 94 \/ n = 95 \/ n = 96 \/ n = 97 \/ n  = 98 \/ n = 99 \/
                        n = 100 \/ n = 101 \/ n = 102 \/ n = 103 \/ n = 104 \/ n = 105 \/ n = 106 \/ n = 107 \/ n  = 108 \/ n = 109 \/
                        n = 110 \/ n = 111 \/ n = 112 \/ n = 113 \/ n = 114 \/ n = 115 \/ n = 116 \/ n = 117 \/ n  = 118 \/ n = 119.
Proof.
  split.
  assert (foo:forall x y : nat, x < S y -> x=y \/ x < y) by (intros; lia).
  intros.
  repeat (match goal with T:?n< S ?i |- _ => let Hequal := fresh in let Hlt := fresh in destruct (foo n i T) as [Hequal | Hlt]; clear T; [tauto|idtac] end).
inversion H0.
lia.
Qed.

Lemma modulo_prop : forall n:nat, exists p:nat, p<120 /\ PeanoNat.Nat.modulo n 120 = p.
Proof.
  intros.
  exists (PeanoNat.Nat.modulo n 120).
  split.
  apply PeanoNat.Nat.mod_bound_pos.
  lia.
  lia.
  reflexivity.
Qed.

Lemma modulo_S : forall n:nat,
    (Nat.modulo (S n) 120 = S (Nat.modulo n 120)) \/ ((Nat.modulo n 120 = 119)/\(Nat.modulo (S n) 120=0)).
Proof.
  intros; apply or_comm;apply modulo_S120.
Qed.

Lemma equiv_bis120 :
  forall P:nat->nat->Prop,
(forall n:nat, P (Nat.modulo n 120) (Nat.modulo (S n) 120)) <->
    (P 0 1/\ P 1 2 /\ P 2 3/\ P 3 4/\ P 4 5/\ P 5 6/\ P 6 7/\ P 7 8/\ P 8 9/\ P 9 10/\
     P 10 11/\ P 11 12/\ P 12 13/\ P 13 14/\ P 14 15/\ P 15 16/\ P 16 17/\ P 17 18/\ P 18 19/\ P 19 20/\
     P 20 21/\ P 21 22/\ P 22 23/\ P 23 24/\ P 24 25/\ P 25 26/\ P 26 27/\ P 27 28/\ P 28 29/\ P 29 30/\
     P 30 31/\ P 31 32/\ P 32 33/\ P 33 34/\ P 34 35/\ P 35 36/\ P 36 37/\ P 37 38/\ P 38 39/\ P 39 40/\
     P 40 41/\ P 41 42/\ P 42 43/\ P 43 44/\ P 44 45/\ P 45 46 /\ P 46 47/\ P 47 48/\ P 48 49/\ P 49 50/\
     P 50 51/\ P 51 52/\ P 52 53/\ P 53 54/\ P 54 55/\ P 55 56 /\ P 56 57/\ P 57 58/\ P 58 59/\ P 59 60/\
     P 60 61/\ P 61 62/\ P 62 63/\ P 63 64/\ P 64 65/\ P 65 66/\ P 66 67/\ P 67 68/\ P 68 69/\ P 69 70/\
     P 70 71/\ P 71 72/\ P 72 73/\ P 73 74/\ P 74 75/\ P 75 76/\ P 76 77/\ P 77 78/\ P 78 79/\ P 79 80/\
     P 80 81/\ P 81 82/\ P 82 83/\ P 83 84/\ P 84 85/\ P 85 86/\ P 86 87/\ P 87 88/\ P 88 89/\ P 89 90/\
     P 90 91/\ P 91 92/\ P 92 93/\ P 93 94/\ P 94 95/\ P 95 96/\ P 96 97/\ P 97 98/\ P 98 99/\ P 99 100/\
     P 100 101/\ P 101 102/\ P 102 103/\ P 103 104/\ P 104 105/\ P 105 106 /\ P 106 107/\ P 107 108/\ P 108 109/\ P 109 110/\
     P 110 111/\ P 111 112/\ P 112 113/\ P 113 114/\ P 114 115/\ P 115 116 /\ P 116 117/\ P 117 118/\ P 118 119/\ P 119 0).
Proof.
intros.
split.
intros.
repeat split;match goal with |- P ?X ?Y   => rewrite <- PeanoNat.Nat.mod_small with (a:=X) (b:=120) by lia end; apply H.
intros.
destruct (modulo_prop n) as [p [Hp Hp']].
destruct (modulo_prop (S n)) as [q [Hq Hq']].
destruct (modulo_S n) as [HA | HB].
rewrite Hp' Hq' in HA.
rewrite Hp' Hq'.
apply n120_decomp in Hp.
apply n120_decomp in Hq.
clear Hp' Hq'.
rewrite HA in Hq.
rewrite HA.
clear n q HA.
decompose [and] H; clear H.
decompose [or] Hp; clear Hp; subst p; try assumption.
decompose [or] Hq; try discriminate.
destruct HB as [HB1 HB2].
rewrite HB1.
rewrite HB2.
intuition.
Qed.

Lemma are_isomorphic_refl : forall s, are_isomorphic s s.
Proof.
  exists (fun (p:Point) => p).
  exists (fun (l:Line) => l).
  split.
  simpl.
  split.
  split.
  unfold inj; destruct x; destruct y; simpl; intros H; solve [discriminate H | reflexivity ].
  unfold surj; destruct y; solve_surjP.
  split.
  split.
  unfold inj; destruct x; destruct y; simpl; intros H; solve [discriminate H | reflexivity ].
  unfold surj; destruct y; solve_surjL.
  intros; assumption.
  intros.
  rewrite map_id.
  rewrite sorted_spreads'.
  assumption.
  split; assumption.
Qed.

Lemma are_isomorphic_trans :
  forall s1 s2 s3, are_isomorphic s1 s2 -> are_isomorphic s2 s3 -> are_isomorphic s1 s3.
Proof.
intros s1 s2 s3 Hs1s2 Hs2s3.
destruct Hs1s2 as [fp [ fl [is_col is_map]]].
destruct Hs2s3 as [fp' [ fl' [is_col' is_map']]].
destruct is_col as [[Hinjp Hsurjp] [[Hinjl Hsurjl] Hcompat]].
destruct is_col' as [[Hinjp' Hsurjp'] [[Hinjl' Hsurjl'] Hcompat']].

exists (fun (x:Point) => fp' (fp x)).
exists (fun (x:Line) => fl' (fl x)).
split.
split.
split.
unfold inj.
intros.
apply Hinjp.
apply Hinjp'.
assumption.
unfold surj.
intros.
unfold surj in *.
destruct (Hsurjp' y).
destruct (Hsurjp x).
exists x0.
rewrite H0 in H.
assumption.
split.
split.
unfold inj.
intros.
apply Hinjl.
apply Hinjl'.
assumption.
unfold surj.
intros.
unfold surj in *.
destruct (Hsurjl' y).
destruct (Hsurjl x).
exists x0.
rewrite H0 in H.
assumption.
intros.
apply Hcompat'.
apply Hcompat.
assumption.

intros.
generalize (is_map s H H0).
intros.
destruct H1.

rewrite <- map_map.
generalize (is_map' _   H1 H2).
intros.
destruct H3.
split.
rewrite sort_map_sort in H3.
assumption.
rewrite sort_map_sort in H4.
assumption.
Qed.

Lemma all_isomorphic_lemma0 :  forall t1 t2 : (list (list Line)), In t1 class0 -> In t2 class0 -> are_isomorphic t1 t2.
Proof.
  apply (all_equiv (list Line)).
  simpl; lia.
  unfold are_isomorphic.
  apply are_isomorphic_refl.
  apply are_isomorphic_trans.
  unfold all_iso_decomp.
  intros n H.
  apply equiv_bis120.
  repeat split.
  exists fp0_3; exists fl0_3; split; [is_col |is_col2].
  exists fp3_5; exists fl3_5; split; [is_col |is_col2].
  exists fp5_6; exists fl5_6; split; [is_col |is_col2].
  exists fp6_9; exists fl6_9; split; [is_col |is_col2].
  exists fp9_11; exists  fl9_11; split; [is_col |is_col2].
  exists fp11_13; exists fl11_13; split; [is_col |is_col2].
  exists fp13_15; exists fl13_15; split; [is_col |is_col2].
  exists fp15_16; exists fl15_16; split; [is_col |is_col2].
  exists fp16_18; exists fl16_18; split; [is_col |is_col2].
  exists fp18_21; exists fl18_21; split; [is_col |is_col2].
  exists fp21_22; exists fl21_22; split; [is_col |is_col2].
  exists fp22_25; exists fl22_25; split; [is_col |is_col2].
  exists fp25_26; exists fl25_26; split; [is_col |is_col2].
  exists fp26_28; exists fl26_28; split; [is_col |is_col2].
  exists fp28_31; exists fl28_31; split; [is_col |is_col2].
  exists fp31_32; exists fl31_32; split; [is_col |is_col2].
  exists fp32_34; exists fl32_34; split; [is_col |is_col2].
  exists fp34_37; exists fl34_37; split; [is_col |is_col2].
  exists fp37_38; exists fl37_38; split; [is_col |is_col2].
  exists fp38_40; exists fl38_40; split; [is_col |is_col2].
  exists fp40_42; exists fl40_42; split; [is_col |is_col2].
  exists fp42_44; exists fl42_44; split; [is_col |is_col2].
  exists fp44_47; exists fl44_47; split; [is_col |is_col2].
  exists fp47_48; exists fl47_48; split; [is_col |is_col2].
  exists fp48_51; exists fl48_51; split; [is_col |is_col2].
  exists fp51_52; exists fl51_52; split; [is_col |is_col2].
  exists fp52_54; exists fl52_54; split; [is_col |is_col2].
  exists fp54_56; exists fl54_56; split; [is_col |is_col2].
  exists fp56_59; exists fl56_59; split; [is_col |is_col2].
  exists fp59_61; exists fl59_61; split; [is_col |is_col2].
  exists fp61_63; exists fl61_63; split; [is_col |is_col2].
  exists fp63_64; exists fl63_64; split; [is_col |is_col2].
  exists fp64_67; exists fl64_67; split; [is_col |is_col2].
  exists fp67_68; exists fl67_68; split; [is_col |is_col2].
  exists fp68_71; exists fl68_71; split; [is_col |is_col2].
  exists fp71_73; exists fl71_73; split; [is_col |is_col2].
  exists fp73_74; exists fl73_74; split; [is_col |is_col2].
  exists fp74_77; exists fl74_77; split; [is_col |is_col2].
  exists fp77_78; exists fl77_78; split; [is_col |is_col2].
  exists fp78_80; exists fl78_80; split; [is_col |is_col2].
  exists fp80_83; exists fl80_83; split; [is_col |is_col2].
  exists fp83_85; exists fl83_85; split; [is_col |is_col2].
  exists fp85_86; exists fl85_86; split; [is_col |is_col2].
  exists fp86_89; exists fl86_89; split; [is_col |is_col2].
  exists fp89_90; exists fl89_90; split; [is_col |is_col2].
  exists fp90_92; exists fl90_92; split; [is_col |is_col2].
  exists fp92_95; exists fl92_95; split; [is_col |is_col2].
  exists fp95_97; exists fl95_97; split; [is_col |is_col2].
  exists fp97_98; exists fl97_98; split; [is_col |is_col2].
  exists fp98_101; exists fl98_101; split; [is_col |is_col2].
  exists fp101_103; exists fl101_103; split; [is_col |is_col2].
  exists fp103_105; exists fl103_105; split; [is_col |is_col2].
  exists fp105_106; exists fl105_106; split; [is_col |is_col2].
  exists fp106_108; exists fl106_108; split; [is_col |is_col2].
  exists fp108_111; exists fl108_111; split; [is_col |is_col2].
  exists fp111_112; exists fl111_112; split; [is_col |is_col2].
  exists fp112_114; exists fl112_114; split; [is_col |is_col2].
  exists fp114_117; exists fl114_117; split; [is_col |is_col2].
  exists fp117_118; exists fl117_118; split; [is_col |is_col2].
  exists fp118_121; exists fl118_121; split; [is_col |is_col2].
  exists fp121_122; exists fl121_122; split; [is_col |is_col2].
  exists fp122_124; exists fl122_124; split; [is_col |is_col2].
  exists fp124_127; exists fl124_127; split; [is_col |is_col2].
  exists fp127_128; exists fl127_128; split; [is_col |is_col2].
  exists fp128_131; exists fl128_131; split; [is_col |is_col2].
  exists fp131_132; exists fl131_132; split; [is_col |is_col2].
  exists fp132_134; exists fl132_134; split; [is_col |is_col2].
  exists fp134_137; exists fl134_137; split; [is_col |is_col2].
  exists fp137_138; exists fl137_138; split; [is_col |is_col2].
  exists fp138_140; exists fl138_140; split; [is_col |is_col2].
  exists fp140_143; exists fl140_143; split; [is_col |is_col2].
  exists fp143_144; exists fl143_144; split; [is_col |is_col2].
  exists fp144_146; exists fl144_146; split; [is_col |is_col2].
  exists fp146_149; exists fl146_149; split; [is_col |is_col2].
  exists fp149_150; exists fl149_150; split; [is_col |is_col2].
  exists fp150_153; exists fl150_153; split; [is_col |is_col2].
  exists fp153_155; exists fl153_155; split; [is_col |is_col2].
  exists fp155_156; exists fl155_156; split; [is_col |is_col2].
  exists fp156_159; exists fl156_159; split; [is_col |is_col2].
  exists fp159_161; exists fl159_161; split; [is_col |is_col2].
  exists fp161_162; exists fl161_162; split; [is_col |is_col2].
  exists fp162_164; exists fl162_164; split; [is_col |is_col2].
  exists fp164_167; exists fl164_167; split; [is_col |is_col2].
  exists fp167_168; exists fl167_168; split; [is_col |is_col2].
  exists fp168_171; exists fl168_171; split; [is_col |is_col2].
  exists fp171_172; exists fl171_172; split; [is_col |is_col2].
  exists fp172_175; exists fl172_175; split; [is_col |is_col2].
  exists fp175_177; exists fl175_177; split; [is_col |is_col2].
  exists fp177_178; exists fl177_178; split; [is_col |is_col2].
  exists fp178_180; exists fl178_180; split; [is_col |is_col2].
  exists fp180_182; exists fl180_182; split; [is_col |is_col2].
  exists fp182_185; exists fl182_185; split; [is_col |is_col2].
  exists fp185_186; exists fl185_186; split; [is_col |is_col2].
  exists fp186_188; exists fl186_188; split; [is_col |is_col2].
  exists fp188_191; exists fl188_191; split; [is_col |is_col2].
  exists fp191_192; exists fl191_192; split; [is_col |is_col2].
  exists fp192_195; exists fl192_195; split; [is_col |is_col2].
  exists fp195_196; exists fl195_196; split; [is_col |is_col2].
  exists fp196_199; exists fl196_199; split; [is_col |is_col2].
  exists fp199_201; exists fl199_201; split; [is_col |is_col2].
  exists fp201_202; exists fl201_202; split; [is_col |is_col2].
  exists fp202_205; exists fl202_205; split; [is_col |is_col2].
  exists fp205_206; exists fl205_206; split; [is_col |is_col2].
  exists fp206_209; exists fl206_209; split; [is_col |is_col2].
  exists fp209_211; exists fl209_211; split; [is_col |is_col2].
  exists fp211_212; exists fl211_212; split; [is_col |is_col2].
  exists fp212_215; exists fl212_215; split; [is_col |is_col2].
  exists fp215_217; exists fl215_217; split; [is_col |is_col2].
  exists fp217_219; exists fl217_219; split; [is_col |is_col2].
  exists fp219_220; exists fl219_220; split; [is_col |is_col2].
  exists fp220_223; exists fl220_223; split; [is_col |is_col2].
  exists fp223_224; exists fl223_224; split; [is_col |is_col2].
  exists fp224_227; exists fl224_227; split; [is_col |is_col2].
  exists fp227_228; exists fl227_228; split; [is_col |is_col2].
  exists fp228_231; exists fl228_231; split; [is_col |is_col2].
  exists fp231_233; exists fl231_233; split; [is_col |is_col2].
  exists fp233_234; exists fl233_234; split; [is_col |is_col2].
  exists fp234_237; exists fl234_237; split; [is_col |is_col2].
  exists fp237_239; exists fl237_239; split; [is_col |is_col2].
  exists fp239_0; exists fl239_0; split; [is_col |is_col2].
Qed.

Lemma all_isomorphic_lemma1 :  forall t1 t2 : (list (list Line)), In t1 class1 -> In t2 class1 -> are_isomorphic t1 t2.
Proof.
  pattern class1; unfold class1; simpl complement.
  apply (all_equiv (list Line)).
  simpl; lia.
  unfold are_isomorphic.
  apply are_isomorphic_refl.
  apply are_isomorphic_trans.
  unfold all_iso_decomp.
  intros n H.
  apply equiv_bis120.
  repeat split.
  exists fp1_2; exists fl1_2; split; [is_col |is_col2].
  exists fp2_4; exists fl2_4; split; [is_col |is_col2].
  exists fp4_7; exists fl4_7; split; [is_col |is_col2].
  exists fp7_8; exists fl7_8; split; [is_col |is_col2].
  exists fp8_10; exists  fl8_10; split; [is_col |is_col2].
  exists fp10_12; exists fl10_12; split; [is_col |is_col2].
  exists fp12_14; exists fl12_14; split; [is_col |is_col2].
  exists fp14_17; exists fl14_17; split; [is_col |is_col2].
  exists fp17_19; exists fl17_19; split; [is_col |is_col2].
  exists fp19_20; exists fl19_20; split; [is_col |is_col2].
  exists fp20_23; exists fl20_23; split; [is_col |is_col2].
  exists fp23_24; exists fl23_24; split; [is_col |is_col2].
  exists fp24_27; exists fl24_27; split; [is_col |is_col2].
  exists fp27_29; exists fl27_29; split; [is_col |is_col2].
  exists fp29_30; exists fl29_30; split; [is_col |is_col2].
  exists fp30_33; exists fl30_33; split; [is_col |is_col2].
  exists fp33_35; exists fl33_35; split; [is_col |is_col2].
  exists fp35_36; exists fl35_36; split; [is_col |is_col2].
  exists fp36_39; exists fl36_39; split; [is_col |is_col2].
  exists fp39_41; exists fl39_41; split; [is_col |is_col2].
  exists fp41_43; exists fl41_43; split; [is_col |is_col2].
  exists fp43_45; exists fl43_45; split; [is_col |is_col2].
  exists fp45_46; exists fl45_46; split; [is_col |is_col2].
  exists fp46_49; exists fl46_49; split; [is_col |is_col2].
  exists fp49_50; exists fl49_50; split; [is_col |is_col2].
  exists fp50_53; exists fl50_53; split; [is_col |is_col2].
  exists fp53_55; exists fl53_55; split; [is_col |is_col2].
  exists fp55_57; exists fl55_57; split; [is_col |is_col2].
  exists fp57_58; exists fl57_58; split; [is_col |is_col2].
  exists fp58_60; exists fl58_60; split; [is_col |is_col2].
  exists fp60_62; exists fl60_62; split; [is_col |is_col2].
  exists fp62_65; exists fl62_65; split; [is_col |is_col2].
  exists fp65_66; exists fl65_66; split; [is_col |is_col2].
  exists fp66_69; exists fl66_69; split; [is_col |is_col2].
  exists fp69_70; exists fl69_70; split; [is_col |is_col2].
  exists fp70_72; exists fl70_72; split; [is_col |is_col2].
  exists fp72_75; exists fl72_75; split; [is_col |is_col2].
  exists fp75_76; exists fl75_76; split; [is_col |is_col2].
  exists fp76_79; exists fl76_79; split; [is_col |is_col2].
  exists fp79_81; exists fl79_81; split; [is_col |is_col2].
  exists fp81_82; exists fl81_82; split; [is_col |is_col2].
  exists fp82_84; exists fl82_84; split; [is_col |is_col2].
  exists fp84_87; exists fl84_87; split; [is_col |is_col2].
  exists fp87_88; exists fl87_88; split; [is_col |is_col2].
  exists fp88_91; exists fl88_91; split; [is_col |is_col2].
  exists fp91_93; exists fl91_93; split; [is_col |is_col2].
  exists fp93_94; exists fl93_94; split; [is_col |is_col2].
  exists fp94_96; exists fl94_96; split; [is_col |is_col2].
  exists fp96_99; exists fl96_99; split; [is_col |is_col2].
  exists fp99_100; exists fl99_100; split; [is_col |is_col2].
  exists fp100_102; exists fl100_102; split; [is_col |is_col2].
  exists fp102_104; exists fl102_104; split; [is_col |is_col2].
  exists fp104_107; exists fl104_107; split; [is_col |is_col2].
  exists fp107_109; exists fl107_109; split; [is_col |is_col2].
  exists fp109_110; exists fl109_110; split; [is_col |is_col2].
  exists fp110_113; exists fl110_113; split; [is_col |is_col2].
  exists fp113_115; exists fl113_115; split; [is_col |is_col2].
  exists fp115_116; exists fl115_116; split; [is_col |is_col2].
  exists fp116_119; exists fl116_119; split; [is_col |is_col2].
  exists fp119_120; exists fl119_120; split; [is_col |is_col2].
  exists fp120_123; exists fl120_123; split; [is_col |is_col2].
  exists fp123_125; exists fl123_125; split; [is_col |is_col2].
  exists fp125_126; exists fl125_126; split; [is_col |is_col2].
  exists fp126_129; exists fl126_129; split; [is_col |is_col2].
  exists fp129_130; exists fl129_130; split; [is_col |is_col2].
  exists fp130_133; exists fl130_133; split; [is_col |is_col2].
  exists fp133_135; exists fl133_135; split; [is_col |is_col2].
  exists fp135_136; exists fl135_136; split; [is_col |is_col2].
  exists fp136_139; exists fl136_139; split; [is_col |is_col2].
  exists fp139_141; exists fl139_141; split; [is_col |is_col2].
  exists fp141_142; exists fl141_142; split; [is_col |is_col2].
  exists fp142_145; exists fl142_145; split; [is_col |is_col2].
  exists fp145_147; exists fl145_147; split; [is_col |is_col2].
  exists fp147_148; exists fl147_148; split; [is_col |is_col2].
  exists fp148_151; exists fl148_151; split; [is_col |is_col2].
  exists fp151_152; exists fl151_152; split; [is_col |is_col2].
  exists fp152_154; exists fl152_154; split; [is_col |is_col2].
  exists fp154_157; exists fl154_157; split; [is_col |is_col2].
  exists fp157_158; exists fl157_158; split; [is_col |is_col2].
  exists fp158_160; exists fl158_160; split; [is_col |is_col2].
  exists fp160_163; exists fl160_163; split; [is_col |is_col2].
  exists fp163_165; exists fl163_165; split; [is_col |is_col2].
  exists fp165_166; exists fl165_166; split; [is_col |is_col2].
  exists fp166_169; exists fl166_169; split; [is_col |is_col2].
  exists fp169_170; exists fl169_170; split; [is_col |is_col2].
  exists fp170_173; exists fl170_173; split; [is_col |is_col2].
  exists fp173_174; exists fl173_174; split; [is_col |is_col2].
  exists fp174_176; exists fl174_176; split; [is_col |is_col2].
  exists fp176_179; exists fl176_179; split; [is_col |is_col2].
  exists fp179_181; exists fl179_181; split; [is_col |is_col2].
  exists fp181_183; exists fl181_183; split; [is_col |is_col2].
  exists fp183_184; exists fl183_184; split; [is_col |is_col2].
  exists fp184_187; exists fl184_187; split; [is_col |is_col2].
  exists fp187_189; exists fl187_189; split; [is_col |is_col2].
  exists fp189_190; exists fl189_190; split; [is_col |is_col2].
  exists fp190_193; exists fl190_193; split; [is_col |is_col2].
  exists fp193_194; exists fl193_194; split; [is_col |is_col2].
  exists fp194_197; exists fl194_197; split; [is_col |is_col2].
  exists fp197_198; exists fl197_198; split; [is_col |is_col2].
  exists fp198_200; exists fl198_200; split; [is_col |is_col2].
  exists fp200_203; exists fl200_203; split; [is_col |is_col2].
  exists fp203_204; exists fl203_204; split; [is_col |is_col2].
  exists fp204_207; exists fl204_207; split; [is_col |is_col2].
  exists fp207_208; exists fl207_208; split; [is_col |is_col2].
  exists fp208_210; exists fl208_210; split; [is_col |is_col2].
  exists fp210_213; exists fl210_213; split; [is_col |is_col2].
  exists fp213_214; exists fl213_214; split; [is_col |is_col2].
  exists fp214_216; exists fl214_216; split; [is_col |is_col2].
  exists fp216_218; exists fl216_218; split; [is_col |is_col2].
  exists fp218_221; exists fl218_221; split; [is_col |is_col2].
  exists fp221_222; exists fl221_222; split; [is_col |is_col2].
  exists fp222_225; exists fl222_225; split; [is_col |is_col2].
  exists fp225_226; exists fl225_226; split; [is_col |is_col2].
  exists fp226_229; exists fl226_229; split; [is_col |is_col2].
  exists fp229_230; exists fl229_230; split; [is_col |is_col2].
  exists fp230_232; exists fl230_232; split; [is_col |is_col2].
  exists fp232_235; exists fl232_235; split; [is_col |is_col2].
  exists fp235_236; exists fl235_236; split; [is_col |is_col2].
  exists fp236_238; exists fl236_238; split; [is_col |is_col2].
  exists fp238_1; exists fl238_1; split; [is_col |is_col2].
Qed.