ProofLaws.path_closed: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_laws.bend as ProofLaws
Lines 620-632 of minebender-game@1.0.0.0/proof_laws.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_laws.bend&start_line=620&end_line=632

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/LAWS.bend as L
import minebender-game@1.0.0.0/proof_inv.bend as PI

# In a closed grid, a zero walk from a revealed cell ends at a revealed cell.
law path_closed:
  for +path: List<&2, T.Pos>
  for +w: Nat
  for +h: Nat
  for +layout: T.Grid(Bool)
  for +g: T.Grid(Bool)
  for +cl: {PI.closed(w, h, layout, g) == True{} : Bool}
  for +s: T.Pos
  for +q: T.Pos
  for gs: {B.at(Bool, False{}, g, s) == True{} : Bool}
  for +wk: {L.zero_walk(path, w, h, layout, s, q) == True{} : Bool}
  {B.at(Bool, False{}, g, q) == True{} : Bool}

Uses (31):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  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=Base/base.bend&name=Nat.is_eq
  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=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=adj_mines
  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=at
  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=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_base.bend&name=and_true_l
  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_copy.bend&name=adjacent_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_inv.bend&name=closed
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_inv.bend&name=closed_use
  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