ProofSolver.loop_none: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_solver.bend as ProofSolver
Lines 2373-2391 of minebender-game@1.0.0.0/proof_solver.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_solver.bend&start_line=2373&end_line=2391

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/solver.bend as S
import minebender-game@1.0.0.0/proof_cells.bend as PS

# When the loop names no cell, every one of its cells has a checked layout
# that mines it.
law loop_none:
  for +hs: List<&2, T.Pos>
  for +found: List<&2, T.Grid(Bool)>
  for +todo: S.Plan
  for +part: T.Grid(Maybe<&2, Bool>)
  for +w: Nat
  for +h: Nat
  for +n: Nat
  for +rows: T.Grid(T.Seen)
  for +its: List<&2, S.Item>
  for e: {S.loop(hs, found, todo, part, S.Ctx{w, h, n, rows, its}) == None{} : Maybe<&2, T.Pos>}
  for +val: {all_valid(S.Ctx{w, h, n, rows, its}, found) == True{} : Bool}
  for +shP: {B.shaped(Maybe<&2, Bool>, w, h, part) == True{} : Bool}
  for +hon: {PS.allp(~PS.WH, ~PS.onb, PS.WH{w, h}, hs) == True{} : Bool}
  for +c: T.Pos
  for m: {B.contains(hs, c) == True{} : Bool}
  Witness(S.Ctx{w, h, n, rows, its}, c)

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Maybe
  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=same
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=shaped
  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=WH
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=allp
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=allp_head
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=allp_tail
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=onb
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=Witness
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=all_valid
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=loop_none.cov
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=or_cases
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=Ctx
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=Item
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=covered
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=loop
  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
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Seen