theory S_R_Spark_Obligation
imports S_R_Spark_User

begin

lemma goal2'1:
  assumes R1:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.rotate_amount__first''
            <= S_R_Spark_Declaration.s_values'' I''
  "
  assumes R2:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.s_values'' I''
            <= S_R_Spark_Declaration.rotate_amount__last''
  "
  assumes R3:
  " S_R_Spark_Declaration.s_values''
    = ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( S_R_Spark_Declaration.round_index__first''
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                              )
                                                                              ( S_R_Spark_Declaration.round_index__first'' + (43 :: int)
                                                                                := (14 :: int)
                                                                              )
                                                                            )
                                                                            ( S_R_Spark_Declaration.round_index__first'' + (44 :: int)
                                                                              := (13 :: int)
                                                                            )
                                                                          )
                                                                          ( S_R_Spark_Declaration.round_index__first'' + (45 :: int)
                                                                            := (13 :: int)
                                                                          )
                                                                        )
                                                                        ( S_R_Spark_Declaration.round_index__first'' + (46 :: int)
                                                                          := (7 :: int)
                                                                        )
                                                                      )
                                                                      ( S_R_Spark_Declaration.round_index__first'' + (47 :: int)
                                                                        := (5 :: int)
                                                                      )
                                                                    )
                                                                    ( S_R_Spark_Declaration.round_index__first'' + (48 :: int)
                                                                      := (15 :: int)
                                                                    )
                                                                  )
                                                                  ( S_R_Spark_Declaration.round_index__first'' + (49 :: int)
                                                                    := (5 :: int)
                                                                  )
                                                                )
                                                                ( S_R_Spark_Declaration.round_index__first'' + (50 :: int)
                                                                  := (8 :: int)
                                                                )
                                                              )
                                                              ( S_R_Spark_Declaration.round_index__first'' + (51 :: int)
                                                                := (11 :: int)
                                                              )
                                                            )
                                                            ( S_R_Spark_Declaration.round_index__first'' + (52 :: int)
                                                              := (14 :: int)
                                                            )
                                                          )
                                                          ( S_R_Spark_Declaration.round_index__first'' + (53 :: int)
                                                            := (14 :: int)
                                                          )
                                                        )
                                                        ( S_R_Spark_Declaration.round_index__first'' + (54 :: int)
                                                          := (6 :: int)
                                                        )
                                                      )
                                                      ( S_R_Spark_Declaration.round_index__first'' + (55 :: int)
                                                        := (14 :: int)
                                                      )
                                                    )
                                                    ( S_R_Spark_Declaration.round_index__first'' + (56 :: int)
                                                      := (6 :: int)
                                                    )
                                                  )
                                                  ( S_R_Spark_Declaration.round_index__first'' + (57 :: int)
                                                    := (9 :: int)
                                                  )
                                                )
                                                ( S_R_Spark_Declaration.round_index__first'' + (58 :: int)
                                                  := (12 :: int)
                                                )
                                              )
                                              ( S_R_Spark_Declaration.round_index__first'' + (59 :: int)
                                                := (9 :: int)
                                              )
                                            )
                                            ( S_R_Spark_Declaration.round_index__first'' + (60 :: int)
                                              := (12 :: int)
                                            )
                                          )
                                          ( S_R_Spark_Declaration.round_index__first'' + (61 :: int)
                                            := (5 :: int)
                                          )
                                        )
                                        ( S_R_Spark_Declaration.round_index__first'' + (62 :: int)
                                          := (15 :: int)
                                        )
                                      )
                                      ( S_R_Spark_Declaration.round_index__first'' + (63 :: int)
                                        := (8 :: int)
                                      )
                                    )
                                    ( S_R_Spark_Declaration.round_index__first'' + (64 :: int)
                                      := (8 :: int)
                                    )
                                  )
                                  ( S_R_Spark_Declaration.round_index__first'' + (65 :: int)
                                    := (5 :: int)
                                  )
                                )
                                ( S_R_Spark_Declaration.round_index__first'' + (66 :: int)
                                  := (12 :: int)
                                )
                              )
                              ( S_R_Spark_Declaration.round_index__first'' + (67 :: int)
                                := (9 :: int)
                              )
                            )
                            ( S_R_Spark_Declaration.round_index__first'' + (68 :: int)
                              := (12 :: int)
                            )
                          )
                          ( S_R_Spark_Declaration.round_index__first'' + (69 :: int)
                            := (5 :: int)
                          )
                        )
                        ( S_R_Spark_Declaration.round_index__first'' + (70 :: int)
                          := (14 :: int)
                        )
                      )
                      ( S_R_Spark_Declaration.round_index__first'' + (71 :: int)
                        := (6 :: int)
                      )
                    )
                    ( S_R_Spark_Declaration.round_index__first'' + (72 :: int)
                      := (8 :: int)
                    )
                  )
                  ( S_R_Spark_Declaration.round_index__first'' + (73 :: int)
                    := (13 :: int)
                  )
                )
                ( S_R_Spark_Declaration.round_index__first'' + (74 :: int)
                  := (6 :: int)
                )
              )
              ( S_R_Spark_Declaration.round_index__first'' + (75 :: int)
                := (5 :: int)
              )
            )
            ( S_R_Spark_Declaration.round_index__first'' + (76 :: int)
              := (15 :: int)
            )
          )
          ( S_R_Spark_Declaration.round_index__first'' + (77 :: int)
            := (13 :: int)
          )
        )
        ( S_R_Spark_Declaration.round_index__first'' + (78 :: int)
          := (11 :: int)
        )
      )
      ( S_R_Spark_Declaration.round_index__first'' + (79 :: int)
        := (11 :: int)
      )
  "
  assumes R4: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes R5:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes R6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R7:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes R8:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R9:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes R10:
  " S_R_Spark_Declaration.round_index__first'' = (0 :: int)
  "
  assumes R11:
  " S_R_Spark_Declaration.round_index__last'' = (79 :: int)
  "
  assumes R12:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R13:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__first''
  "
  assumes R14:
  " S_R_Spark_Declaration.round_index__last''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R15:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes R16:
  " S_R_Spark_Declaration.rotate_amount__first'' = (0 :: int)
  "
  assumes R17:
  " S_R_Spark_Declaration.rotate_amount__last'' = (15 :: int)
  "
  assumes R18:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R19:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__first''
  "
  assumes R20:
  " S_R_Spark_Declaration.rotate_amount__last''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R21:
  " ALL ( i1'' :: int ) ( v'' :: int )
    .   ( S_R_Spark_Declaration.rotate_definition___mk_const_arr' v'' ) i1''
        = v''
  "
  assumes H1: " (0 :: int) <= S_R_Spark_Declaration.j'' "
  assumes H2: " S_R_Spark_Declaration.j'' <= (79 :: int) "
  assumes H3: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes H4:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes H5:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes H7:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H8:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes H9:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H10:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes H11:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes H12:
  " S_R_Spark_Declaration.round_index__base__first'' <= (0 :: int)
  "
  assumes H13:
  " (79 :: int) <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H14:
  " S_R_Spark_Declaration.rotate_amount__base__first'' <= (0 :: int)
  "
  assumes H15:
  " (15 :: int) <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  shows " ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( (0 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (43 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (44 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (45 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                              )
                                                                              ( (46 :: int)
                                                                                := (7 :: int)
                                                                              )
                                                                            )
                                                                            ( (47 :: int)
                                                                              := (5 :: int)
                                                                            )
                                                                          )
                                                                          ( (48 :: int)
                                                                            := (15 :: int)
                                                                          )
                                                                        )
                                                                        ( (49 :: int)
                                                                          := (5 :: int)
                                                                        )
                                                                      )
                                                                      ( (50 :: int)
                                                                        := (8 :: int)
                                                                      )
                                                                    )
                                                                    ( (51 :: int)
                                                                      := (11 :: int)
                                                                    )
                                                                  )
                                                                  ( (52 :: int)
                                                                    := (14 :: int)
                                                                  )
                                                                )
                                                                ( (53 :: int)
                                                                  := (14 :: int)
                                                                )
                                                              )
                                                              ( (54 :: int)
                                                                := (6 :: int)
                                                              )
                                                            )
                                                            ( (55 :: int)
                                                              := (14 :: int)
                                                            )
                                                          )
                                                          ( (56 :: int)
                                                            := (6 :: int)
                                                          )
                                                        )
                                                        ( (57 :: int)
                                                          := (9 :: int)
                                                        )
                                                      )
                                                      ( (58 :: int)
                                                        := (12 :: int)
                                                      )
                                                    )
                                                    ( (59 :: int)
                                                      := (9 :: int)
                                                    )
                                                  )
                                                  ( (60 :: int)
                                                    := (12 :: int)
                                                  )
                                                )
                                                ( (61 :: int)
                                                  := (5 :: int)
                                                )
                                              )
                                              ( (62 :: int)
                                                := (15 :: int)
                                              )
                                            )
                                            ( (63 :: int)
                                              := (8 :: int)
                                            )
                                          )
                                          ( (64 :: int)
                                            := (8 :: int)
                                          )
                                        )
                                        ( (65 :: int)
                                          := (5 :: int)
                                        )
                                      )
                                      ( (66 :: int)
                                        := (12 :: int)
                                      )
                                    )
                                    ( (67 :: int)
                                      := (9 :: int)
                                    )
                                  )
                                  ( (68 :: int)
                                    := (12 :: int)
                                  )
                                )
                                ( (69 :: int)
                                  := (5 :: int)
                                )
                              )
                              ( (70 :: int)
                                := (14 :: int)
                              )
                            )
                            ( (71 :: int)
                              := (6 :: int)
                            )
                          )
                          ( (72 :: int)
                            := (8 :: int)
                          )
                        )
                        ( (73 :: int)
                          := (13 :: int)
                        )
                      )
                      ( (74 :: int)
                        := (6 :: int)
                      )
                    )
                    ( (75 :: int)
                      := (5 :: int)
                    )
                  )
                  ( (76 :: int)
                    := (15 :: int)
                  )
                )
                ( (77 :: int)
                  := (13 :: int)
                )
              )
              ( (78 :: int)
                := (11 :: int)
              )
            )
            ( (79 :: int)
              := (11 :: int)
            )
          )
            S_R_Spark_Declaration.j''
          = S_R_Spark_Specification.s_r' S_R_Spark_Declaration.j''
        " (is "?C1")
apply (insert assms) by (rule userlemmas)

lemma goal2'2:
  assumes R1:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.rotate_amount__first''
            <= S_R_Spark_Declaration.s_values'' I''
  "
  assumes R2:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.s_values'' I''
            <= S_R_Spark_Declaration.rotate_amount__last''
  "
  assumes R3:
  " S_R_Spark_Declaration.s_values''
    = ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( S_R_Spark_Declaration.round_index__first''
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                              )
                                                                              ( S_R_Spark_Declaration.round_index__first'' + (43 :: int)
                                                                                := (14 :: int)
                                                                              )
                                                                            )
                                                                            ( S_R_Spark_Declaration.round_index__first'' + (44 :: int)
                                                                              := (13 :: int)
                                                                            )
                                                                          )
                                                                          ( S_R_Spark_Declaration.round_index__first'' + (45 :: int)
                                                                            := (13 :: int)
                                                                          )
                                                                        )
                                                                        ( S_R_Spark_Declaration.round_index__first'' + (46 :: int)
                                                                          := (7 :: int)
                                                                        )
                                                                      )
                                                                      ( S_R_Spark_Declaration.round_index__first'' + (47 :: int)
                                                                        := (5 :: int)
                                                                      )
                                                                    )
                                                                    ( S_R_Spark_Declaration.round_index__first'' + (48 :: int)
                                                                      := (15 :: int)
                                                                    )
                                                                  )
                                                                  ( S_R_Spark_Declaration.round_index__first'' + (49 :: int)
                                                                    := (5 :: int)
                                                                  )
                                                                )
                                                                ( S_R_Spark_Declaration.round_index__first'' + (50 :: int)
                                                                  := (8 :: int)
                                                                )
                                                              )
                                                              ( S_R_Spark_Declaration.round_index__first'' + (51 :: int)
                                                                := (11 :: int)
                                                              )
                                                            )
                                                            ( S_R_Spark_Declaration.round_index__first'' + (52 :: int)
                                                              := (14 :: int)
                                                            )
                                                          )
                                                          ( S_R_Spark_Declaration.round_index__first'' + (53 :: int)
                                                            := (14 :: int)
                                                          )
                                                        )
                                                        ( S_R_Spark_Declaration.round_index__first'' + (54 :: int)
                                                          := (6 :: int)
                                                        )
                                                      )
                                                      ( S_R_Spark_Declaration.round_index__first'' + (55 :: int)
                                                        := (14 :: int)
                                                      )
                                                    )
                                                    ( S_R_Spark_Declaration.round_index__first'' + (56 :: int)
                                                      := (6 :: int)
                                                    )
                                                  )
                                                  ( S_R_Spark_Declaration.round_index__first'' + (57 :: int)
                                                    := (9 :: int)
                                                  )
                                                )
                                                ( S_R_Spark_Declaration.round_index__first'' + (58 :: int)
                                                  := (12 :: int)
                                                )
                                              )
                                              ( S_R_Spark_Declaration.round_index__first'' + (59 :: int)
                                                := (9 :: int)
                                              )
                                            )
                                            ( S_R_Spark_Declaration.round_index__first'' + (60 :: int)
                                              := (12 :: int)
                                            )
                                          )
                                          ( S_R_Spark_Declaration.round_index__first'' + (61 :: int)
                                            := (5 :: int)
                                          )
                                        )
                                        ( S_R_Spark_Declaration.round_index__first'' + (62 :: int)
                                          := (15 :: int)
                                        )
                                      )
                                      ( S_R_Spark_Declaration.round_index__first'' + (63 :: int)
                                        := (8 :: int)
                                      )
                                    )
                                    ( S_R_Spark_Declaration.round_index__first'' + (64 :: int)
                                      := (8 :: int)
                                    )
                                  )
                                  ( S_R_Spark_Declaration.round_index__first'' + (65 :: int)
                                    := (5 :: int)
                                  )
                                )
                                ( S_R_Spark_Declaration.round_index__first'' + (66 :: int)
                                  := (12 :: int)
                                )
                              )
                              ( S_R_Spark_Declaration.round_index__first'' + (67 :: int)
                                := (9 :: int)
                              )
                            )
                            ( S_R_Spark_Declaration.round_index__first'' + (68 :: int)
                              := (12 :: int)
                            )
                          )
                          ( S_R_Spark_Declaration.round_index__first'' + (69 :: int)
                            := (5 :: int)
                          )
                        )
                        ( S_R_Spark_Declaration.round_index__first'' + (70 :: int)
                          := (14 :: int)
                        )
                      )
                      ( S_R_Spark_Declaration.round_index__first'' + (71 :: int)
                        := (6 :: int)
                      )
                    )
                    ( S_R_Spark_Declaration.round_index__first'' + (72 :: int)
                      := (8 :: int)
                    )
                  )
                  ( S_R_Spark_Declaration.round_index__first'' + (73 :: int)
                    := (13 :: int)
                  )
                )
                ( S_R_Spark_Declaration.round_index__first'' + (74 :: int)
                  := (6 :: int)
                )
              )
              ( S_R_Spark_Declaration.round_index__first'' + (75 :: int)
                := (5 :: int)
              )
            )
            ( S_R_Spark_Declaration.round_index__first'' + (76 :: int)
              := (15 :: int)
            )
          )
          ( S_R_Spark_Declaration.round_index__first'' + (77 :: int)
            := (13 :: int)
          )
        )
        ( S_R_Spark_Declaration.round_index__first'' + (78 :: int)
          := (11 :: int)
        )
      )
      ( S_R_Spark_Declaration.round_index__first'' + (79 :: int)
        := (11 :: int)
      )
  "
  assumes R4: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes R5:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes R6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R7:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes R8:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R9:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes R10:
  " S_R_Spark_Declaration.round_index__first'' = (0 :: int)
  "
  assumes R11:
  " S_R_Spark_Declaration.round_index__last'' = (79 :: int)
  "
  assumes R12:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R13:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__first''
  "
  assumes R14:
  " S_R_Spark_Declaration.round_index__last''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R15:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes R16:
  " S_R_Spark_Declaration.rotate_amount__first'' = (0 :: int)
  "
  assumes R17:
  " S_R_Spark_Declaration.rotate_amount__last'' = (15 :: int)
  "
  assumes R18:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R19:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__first''
  "
  assumes R20:
  " S_R_Spark_Declaration.rotate_amount__last''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R21:
  " ALL ( i1'' :: int ) ( v'' :: int )
    .   ( S_R_Spark_Declaration.rotate_definition___mk_const_arr' v'' ) i1''
        = v''
  "
  assumes H1: " (0 :: int) <= S_R_Spark_Declaration.j'' "
  assumes H2: " S_R_Spark_Declaration.j'' <= (79 :: int) "
  assumes H3: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes H4:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes H5:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes H7:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H8:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes H9:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H10:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes H11:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes H12:
  " S_R_Spark_Declaration.round_index__base__first'' <= (0 :: int)
  "
  assumes H13:
  " (79 :: int) <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H14:
  " S_R_Spark_Declaration.rotate_amount__base__first'' <= (0 :: int)
  "
  assumes H15:
  " (15 :: int) <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  shows " (0 :: int)
          <= ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( (0 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (43 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (44 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (45 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (46 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                               )
                                                                               ( (47 :: int)
                                                                                := (5 :: int)
                                                                               )
                                                                             )
                                                                             ( (48 :: int)
                                                                               := (15 :: int)
                                                                             )
                                                                           )
                                                                           ( (49 :: int)
                                                                             := (5 :: int)
                                                                           )
                                                                         )
                                                                         ( (50 :: int)
                                                                           := (8 :: int)
                                                                         )
                                                                       )
                                                                       ( (51 :: int)
                                                                         := (11 :: int)
                                                                       )
                                                                     )
                                                                     ( (52 :: int)
                                                                       := (14 :: int)
                                                                     )
                                                                   )
                                                                   ( (53 :: int)
                                                                     := (14 :: int)
                                                                   )
                                                                 )
                                                                 ( (54 :: int)
                                                                   := (6 :: int)
                                                                 )
                                                               )
                                                               ( (55 :: int)
                                                                 := (14 :: int)
                                                               )
                                                             )
                                                             ( (56 :: int)
                                                               := (6 :: int)
                                                             )
                                                           )
                                                           ( (57 :: int)
                                                             := (9 :: int)
                                                           )
                                                         )
                                                         ( (58 :: int)
                                                           := (12 :: int)
                                                         )
                                                       )
                                                       ( (59 :: int)
                                                         := (9 :: int)
                                                       )
                                                     )
                                                     ( (60 :: int)
                                                       := (12 :: int)
                                                     )
                                                   )
                                                   ( (61 :: int)
                                                     := (5 :: int)
                                                   )
                                                 )
                                                 ( (62 :: int)
                                                   := (15 :: int)
                                                 )
                                               )
                                               ( (63 :: int)
                                                 := (8 :: int)
                                               )
                                             )
                                             ( (64 :: int)
                                               := (8 :: int)
                                             )
                                           )
                                           ( (65 :: int)
                                             := (5 :: int)
                                           )
                                         )
                                         ( (66 :: int)
                                           := (12 :: int)
                                         )
                                       )
                                       ( (67 :: int)
                                         := (9 :: int)
                                       )
                                     )
                                     ( (68 :: int)
                                       := (12 :: int)
                                     )
                                   )
                                   ( (69 :: int)
                                     := (5 :: int)
                                   )
                                 )
                                 ( (70 :: int)
                                   := (14 :: int)
                                 )
                               )
                               ( (71 :: int)
                                 := (6 :: int)
                               )
                             )
                             ( (72 :: int)
                               := (8 :: int)
                             )
                           )
                           ( (73 :: int)
                             := (13 :: int)
                           )
                         )
                         ( (74 :: int)
                           := (6 :: int)
                         )
                       )
                       ( (75 :: int)
                         := (5 :: int)
                       )
                     )
                     ( (76 :: int)
                       := (15 :: int)
                     )
                   )
                   ( (77 :: int)
                     := (13 :: int)
                   )
                 )
                 ( (78 :: int)
                   := (11 :: int)
                 )
               )
               ( (79 :: int)
                 := (11 :: int)
               )
             )
               S_R_Spark_Declaration.j''
        " (is "?C1")
apply (insert assms) by (rule userlemmas)

lemma goal2'3:
  assumes R1:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.rotate_amount__first''
            <= S_R_Spark_Declaration.s_values'' I''
  "
  assumes R2:
  " ALL ( I'' :: int )
    .   (0 :: int) <= I'' & I'' <= (79 :: int)
        --> S_R_Spark_Declaration.s_values'' I''
            <= S_R_Spark_Declaration.rotate_amount__last''
  "
  assumes R3:
  " S_R_Spark_Declaration.s_values''
    = ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( S_R_Spark_Declaration.round_index__first''
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( S_R_Spark_Declaration.round_index__first'' + (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                              )
                                                                              ( S_R_Spark_Declaration.round_index__first'' + (43 :: int)
                                                                                := (14 :: int)
                                                                              )
                                                                            )
                                                                            ( S_R_Spark_Declaration.round_index__first'' + (44 :: int)
                                                                              := (13 :: int)
                                                                            )
                                                                          )
                                                                          ( S_R_Spark_Declaration.round_index__first'' + (45 :: int)
                                                                            := (13 :: int)
                                                                          )
                                                                        )
                                                                        ( S_R_Spark_Declaration.round_index__first'' + (46 :: int)
                                                                          := (7 :: int)
                                                                        )
                                                                      )
                                                                      ( S_R_Spark_Declaration.round_index__first'' + (47 :: int)
                                                                        := (5 :: int)
                                                                      )
                                                                    )
                                                                    ( S_R_Spark_Declaration.round_index__first'' + (48 :: int)
                                                                      := (15 :: int)
                                                                    )
                                                                  )
                                                                  ( S_R_Spark_Declaration.round_index__first'' + (49 :: int)
                                                                    := (5 :: int)
                                                                  )
                                                                )
                                                                ( S_R_Spark_Declaration.round_index__first'' + (50 :: int)
                                                                  := (8 :: int)
                                                                )
                                                              )
                                                              ( S_R_Spark_Declaration.round_index__first'' + (51 :: int)
                                                                := (11 :: int)
                                                              )
                                                            )
                                                            ( S_R_Spark_Declaration.round_index__first'' + (52 :: int)
                                                              := (14 :: int)
                                                            )
                                                          )
                                                          ( S_R_Spark_Declaration.round_index__first'' + (53 :: int)
                                                            := (14 :: int)
                                                          )
                                                        )
                                                        ( S_R_Spark_Declaration.round_index__first'' + (54 :: int)
                                                          := (6 :: int)
                                                        )
                                                      )
                                                      ( S_R_Spark_Declaration.round_index__first'' + (55 :: int)
                                                        := (14 :: int)
                                                      )
                                                    )
                                                    ( S_R_Spark_Declaration.round_index__first'' + (56 :: int)
                                                      := (6 :: int)
                                                    )
                                                  )
                                                  ( S_R_Spark_Declaration.round_index__first'' + (57 :: int)
                                                    := (9 :: int)
                                                  )
                                                )
                                                ( S_R_Spark_Declaration.round_index__first'' + (58 :: int)
                                                  := (12 :: int)
                                                )
                                              )
                                              ( S_R_Spark_Declaration.round_index__first'' + (59 :: int)
                                                := (9 :: int)
                                              )
                                            )
                                            ( S_R_Spark_Declaration.round_index__first'' + (60 :: int)
                                              := (12 :: int)
                                            )
                                          )
                                          ( S_R_Spark_Declaration.round_index__first'' + (61 :: int)
                                            := (5 :: int)
                                          )
                                        )
                                        ( S_R_Spark_Declaration.round_index__first'' + (62 :: int)
                                          := (15 :: int)
                                        )
                                      )
                                      ( S_R_Spark_Declaration.round_index__first'' + (63 :: int)
                                        := (8 :: int)
                                      )
                                    )
                                    ( S_R_Spark_Declaration.round_index__first'' + (64 :: int)
                                      := (8 :: int)
                                    )
                                  )
                                  ( S_R_Spark_Declaration.round_index__first'' + (65 :: int)
                                    := (5 :: int)
                                  )
                                )
                                ( S_R_Spark_Declaration.round_index__first'' + (66 :: int)
                                  := (12 :: int)
                                )
                              )
                              ( S_R_Spark_Declaration.round_index__first'' + (67 :: int)
                                := (9 :: int)
                              )
                            )
                            ( S_R_Spark_Declaration.round_index__first'' + (68 :: int)
                              := (12 :: int)
                            )
                          )
                          ( S_R_Spark_Declaration.round_index__first'' + (69 :: int)
                            := (5 :: int)
                          )
                        )
                        ( S_R_Spark_Declaration.round_index__first'' + (70 :: int)
                          := (14 :: int)
                        )
                      )
                      ( S_R_Spark_Declaration.round_index__first'' + (71 :: int)
                        := (6 :: int)
                      )
                    )
                    ( S_R_Spark_Declaration.round_index__first'' + (72 :: int)
                      := (8 :: int)
                    )
                  )
                  ( S_R_Spark_Declaration.round_index__first'' + (73 :: int)
                    := (13 :: int)
                  )
                )
                ( S_R_Spark_Declaration.round_index__first'' + (74 :: int)
                  := (6 :: int)
                )
              )
              ( S_R_Spark_Declaration.round_index__first'' + (75 :: int)
                := (5 :: int)
              )
            )
            ( S_R_Spark_Declaration.round_index__first'' + (76 :: int)
              := (15 :: int)
            )
          )
          ( S_R_Spark_Declaration.round_index__first'' + (77 :: int)
            := (13 :: int)
          )
        )
        ( S_R_Spark_Declaration.round_index__first'' + (78 :: int)
          := (11 :: int)
        )
      )
      ( S_R_Spark_Declaration.round_index__first'' + (79 :: int)
        := (11 :: int)
      )
  "
  assumes R4: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes R5:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes R6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R7:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes R8:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes R9:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes R10:
  " S_R_Spark_Declaration.round_index__first'' = (0 :: int)
  "
  assumes R11:
  " S_R_Spark_Declaration.round_index__last'' = (79 :: int)
  "
  assumes R12:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R13:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__first''
  "
  assumes R14:
  " S_R_Spark_Declaration.round_index__last''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes R15:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes R16:
  " S_R_Spark_Declaration.rotate_amount__first'' = (0 :: int)
  "
  assumes R17:
  " S_R_Spark_Declaration.rotate_amount__last'' = (15 :: int)
  "
  assumes R18:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R19:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__first''
  "
  assumes R20:
  " S_R_Spark_Declaration.rotate_amount__last''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes R21:
  " ALL ( i1'' :: int ) ( v'' :: int )
    .   ( S_R_Spark_Declaration.rotate_definition___mk_const_arr' v'' ) i1''
        = v''
  "
  assumes H1: " (0 :: int) <= S_R_Spark_Declaration.j'' "
  assumes H2: " S_R_Spark_Declaration.j'' <= (79 :: int) "
  assumes H3: " (0 :: int) <= S_R_Spark_Declaration.integer__size'' "
  assumes H4:
  " S_R_Spark_Declaration.integer__first'' <= S_R_Spark_Declaration.integer__last''
  "
  assumes H5:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H6:
  " S_R_Spark_Declaration.integer__base__first''
    <= S_R_Spark_Declaration.integer__first''
  "
  assumes H7:
  " S_R_Spark_Declaration.integer__last''
    <= S_R_Spark_Declaration.integer__base__last''
  "
  assumes H8:
  " (0 :: int) <= S_R_Spark_Declaration.round_index__size''
  "
  assumes H9:
  " S_R_Spark_Declaration.round_index__base__first''
    <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H10:
  " (0 :: int) <= S_R_Spark_Declaration.rotate_amount__size''
  "
  assumes H11:
  " S_R_Spark_Declaration.rotate_amount__base__first''
    <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  assumes H12:
  " S_R_Spark_Declaration.round_index__base__first'' <= (0 :: int)
  "
  assumes H13:
  " (79 :: int) <= S_R_Spark_Declaration.round_index__base__last''
  "
  assumes H14:
  " S_R_Spark_Declaration.rotate_amount__base__first'' <= (0 :: int)
  "
  assumes H15:
  " (15 :: int) <= S_R_Spark_Declaration.rotate_amount__base__last''
  "
  shows " ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( S_R_Spark_Declaration.rotate_definition___default_arr''
                                                                                ( (0 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (1 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (2 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (3 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (4 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (5 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (6 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (7 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (8 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (9 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (10 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (11 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (12 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (13 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (14 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (15 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (16 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (17 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (18 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (19 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (20 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (21 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (22 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (23 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (24 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (25 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (26 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (27 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (28 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (29 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (30 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (31 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (32 :: int)
                                                                                := (9 :: int)
                                                                                )
                                                                                )
                                                                                ( (33 :: int)
                                                                                := (7 :: int)
                                                                                )
                                                                                )
                                                                                ( (34 :: int)
                                                                                := (15 :: int)
                                                                                )
                                                                                )
                                                                                ( (35 :: int)
                                                                                := (11 :: int)
                                                                                )
                                                                                )
                                                                                ( (36 :: int)
                                                                                := (8 :: int)
                                                                                )
                                                                                )
                                                                                ( (37 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (38 :: int)
                                                                                := (6 :: int)
                                                                                )
                                                                                )
                                                                                ( (39 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (40 :: int)
                                                                                := (12 :: int)
                                                                                )
                                                                                )
                                                                                ( (41 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (42 :: int)
                                                                                := (5 :: int)
                                                                                )
                                                                                )
                                                                                ( (43 :: int)
                                                                                := (14 :: int)
                                                                                )
                                                                                )
                                                                                ( (44 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                                )
                                                                                ( (45 :: int)
                                                                                := (13 :: int)
                                                                                )
                                                                              )
                                                                              ( (46 :: int)
                                                                                := (7 :: int)
                                                                              )
                                                                            )
                                                                            ( (47 :: int)
                                                                              := (5 :: int)
                                                                            )
                                                                          )
                                                                          ( (48 :: int)
                                                                            := (15 :: int)
                                                                          )
                                                                        )
                                                                        ( (49 :: int)
                                                                          := (5 :: int)
                                                                        )
                                                                      )
                                                                      ( (50 :: int)
                                                                        := (8 :: int)
                                                                      )
                                                                    )
                                                                    ( (51 :: int)
                                                                      := (11 :: int)
                                                                    )
                                                                  )
                                                                  ( (52 :: int)
                                                                    := (14 :: int)
                                                                  )
                                                                )
                                                                ( (53 :: int)
                                                                  := (14 :: int)
                                                                )
                                                              )
                                                              ( (54 :: int)
                                                                := (6 :: int)
                                                              )
                                                            )
                                                            ( (55 :: int)
                                                              := (14 :: int)
                                                            )
                                                          )
                                                          ( (56 :: int)
                                                            := (6 :: int)
                                                          )
                                                        )
                                                        ( (57 :: int)
                                                          := (9 :: int)
                                                        )
                                                      )
                                                      ( (58 :: int)
                                                        := (12 :: int)
                                                      )
                                                    )
                                                    ( (59 :: int)
                                                      := (9 :: int)
                                                    )
                                                  )
                                                  ( (60 :: int)
                                                    := (12 :: int)
                                                  )
                                                )
                                                ( (61 :: int)
                                                  := (5 :: int)
                                                )
                                              )
                                              ( (62 :: int)
                                                := (15 :: int)
                                              )
                                            )
                                            ( (63 :: int)
                                              := (8 :: int)
                                            )
                                          )
                                          ( (64 :: int)
                                            := (8 :: int)
                                          )
                                        )
                                        ( (65 :: int)
                                          := (5 :: int)
                                        )
                                      )
                                      ( (66 :: int)
                                        := (12 :: int)
                                      )
                                    )
                                    ( (67 :: int)
                                      := (9 :: int)
                                    )
                                  )
                                  ( (68 :: int)
                                    := (12 :: int)
                                  )
                                )
                                ( (69 :: int)
                                  := (5 :: int)
                                )
                              )
                              ( (70 :: int)
                                := (14 :: int)
                              )
                            )
                            ( (71 :: int)
                              := (6 :: int)
                            )
                          )
                          ( (72 :: int)
                            := (8 :: int)
                          )
                        )
                        ( (73 :: int)
                          := (13 :: int)
                        )
                      )
                      ( (74 :: int)
                        := (6 :: int)
                      )
                    )
                    ( (75 :: int)
                      := (5 :: int)
                    )
                  )
                  ( (76 :: int)
                    := (15 :: int)
                  )
                )
                ( (77 :: int)
                  := (13 :: int)
                )
              )
              ( (78 :: int)
                := (11 :: int)
              )
            )
            ( (79 :: int)
              := (11 :: int)
            )
          )
            S_R_Spark_Declaration.j''
          <= (15 :: int)
        " (is "?C1")
apply (insert assms) by (rule userlemmas)
end