def firsts_rows.go

minebender-game@1.0.0.0 · proof_gen.bend:749

import Base
import minebender-game@1.0.0.0/types.bend as T
import minebender-game@1.0.0.0/board.bend as B
import minebender-game@1.0.0.0/game.bend as G

749def firsts_rows.go(+fx: Nat, +fy: Nat, +w: Nat, +y: Nat, +t: List<&2, Nat>,
750  c1: {cnt(fx, List.range(w)) == 1n : Nat},
751  ih: {outs(G.Zone{T.Pos{fx, fy}, False{}}, B.cells.go(w, t)) == cnt(fy, t) : Nat}) ->
752  {outs(G.Zone{T.Pos{fx, fy}, False{}}, List.append(&2, T.Pos, B.row_cells(y, List.range(w)), B.cells.go(w, t)))
753    == cnt(fy, y <> t) : Nat}:
754  +row = B.row_cells(y, List.range(w))
755  %Equal.sym(Nat, outs(G.Zone{T.Pos{fx, fy}, False{}}, List.append(&2, T.Pos, row, B.cells.go(w, t))),
756    Nat.add(outs(G.Zone{T.Pos{fx, fy}, False{}}, row), outs(G.Zone{T.Pos{fx, fy}, False{}}, B.cells.go(w, t))),
757    firsts_append(G.Zone{T.Pos{fx, fy}, False{}}, row, B.cells.go(w, t))) : {_ == cnt(fy, y <> t) : Nat}
758  %Equal.sym(Nat, outs(G.Zone{T.Pos{fx, fy}, False{}}, row), Bool.pick(Nat, Nat.is_eq(y, fy), cnt(fx, List.range(w)), 0n),
759    firsts_row.go(fx, fy, y, List.range(w), Nat.is_eq(y, fy), {==})) :
760    {Nat.add(_, outs(G.Zone{T.Pos{fx, fy}, False{}}, B.cells.go(w, t))) == cnt(fy, y <> t) : Nat}
761  %Equal.sym(Nat, cnt(fx, List.range(w)), 1n, c1) :
762    {Nat.add(Bool.pick(Nat, Nat.is_eq(y, fy), _, 0n), outs(G.Zone{T.Pos{fx, fy}, False{}}, B.cells.go(w, t)))
763      == cnt(fy, y <> t) : Nat}
764  %Equal.sym(Nat, outs(G.Zone{T.Pos{fx, fy}, False{}}, B.cells.go(w, t)), cnt(fy, t), ih) :
765    {Nat.add(Bool.pick(Nat, Nat.is_eq(y, fy), 1n, 0n), _) == cnt(fy, y <> t) : Nat}
766  {==}