def sum_eq_cells

minebender-game@1.0.0.0 · proof_solver.bend:323

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_sums.bend as PU

323def sum_eq_cells(~A: Data, ~f: A -> Nat, +d: A, +w: Nat, +h: Nat, +g: T.Grid(A), +x: Nat,
324  sh: {B.shaped(A, w, h, g) == True{} : Bool}, e: {x == PU.gsum(~A, ~f, g) : Nat}) ->
325  {x == PU.csum(~A, ~f, d, g, B.cells(w, h)) : Nat}:
326  Equal.trans(Nat, x, PU.gsum(~A, ~f, g), PU.csum(~A, ~f, d, g, B.cells(w, h)), e,
327    Equal.sym(Nat, PU.csum(~A, ~f, d, g, B.cells(w, h)), PU.gsum(~A, ~f, g), PU.grid_sum(~A, ~f, d, w, h, g, sh)))