def cells_len

minebender-game@1.0.0.0 · proof_gen.bend:1137

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/proof_base.bend as P

1137def cells_len(+w: Nat, +h: Nat) -> {List.length(&2, T.Pos, B.cells(w, h)) == Nat.mul(w, h) : Nat}:
1138  Equal.trans(Nat, List.length(&2, T.Pos, B.cells(w, h)),
1139    Nat.mul(List.length(&2, Nat, List.range(h)), w), Nat.mul(w, h),
1140    cells_go_len(w, List.range(h)),
1141    %Equal.sym(Nat, List.length(&2, Nat, List.range(h)), h, P.range_length(h)) :
1142      {Nat.mul(_, w) == Nat.mul(w, h) : Nat};
1143      P.mul_comm(h, w))