ProofCells.count_zero_member: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_cells.bend as ProofCells
Lines 578-585 of minebender-game@1.0.0.0/proof_cells.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_cells.bend&start_line=578&end_line=585

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

# A list with no mines has no mine on any of its cells.
law count_zero_member:
  for +layout: T.Grid(Bool)
  for +ns: List<&2, T.Pos>
  for +r: T.Pos
  for +z: {B.count_mines(layout, ns) == 0n : Nat}
  for m: {B.contains(ns, r) == True{} : Bool}
  {B.mine(layout, r) == False{} : Bool}

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=contains
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=count_mines
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=mine
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=same
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=add_zero_l
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=add_zero_r
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=count_zero_member.go
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=one_zero
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Grid
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Pos