ProofWalk.walk_safe: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_walk.bend as ProofWalk
Lines 178-188 of minebender-game@1.0.0.0/proof_walk.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_walk.bend&start_line=178&end_line=188

import Base
import minebender-game@1.0.0.0/types.bend as T
import minebender-game@1.0.0.0/LAWS.bend as L

# A walk from a safe cell only reaches safe cells.
law walk_safe:
  for +path: List<&2, T.Pos>
  for +w: Nat
  for +h: Nat
  for +layout: T.Grid(Bool)
  for +s: T.Pos
  for +q: T.Pos
  for +wk: {L.zero_walk(path, w, h, layout, s, q) == True{} : Bool}
  for +safe: {L.mine(layout, s) == False{} : Bool}
  {L.mine(layout, q) == False{} : Bool}

Uses (25):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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/LAWS.bend&name=adjacent
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=mine
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=on_board
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=zero
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=zero_walk
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=adjacent
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=on_board
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=zero
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=neighbours_member
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=zero_nbr
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_copy.bend&name=adjacent_eq
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_copy.bend&name=mine_eq
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_copy.bend&name=on_board_eq
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_copy.bend&name=zero_eq
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_walk.bend&name=and4_a
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_walk.bend&name=and4_b
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_walk.bend&name=and4_c
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_walk.bend&name=and4_d
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_walk.bend&name=lsame_sound
  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