ProofSolver.dfs_none: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_solver.bend as ProofSolver
Lines 1018-1038 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=1018&end_line=1038

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

# If the search finds nothing, no consistent layout completes the partial
# layout (given that every unassigned cell is still to do).
law dfs_none:
  for +todo: List<&2, S.Todo>
  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 +layout: T.Grid(Bool)
  for e: {S.dfs(todo, part, S.Ctx{w, h, n, rows, its}) == None{} : Maybe<&2, T.Grid(Bool)>}
  for +shP: {B.shaped(Maybe<&2, Bool>, w, h, part) == True{} : Bool}
  for +shL: {B.shaped(Bool, w, h, layout) == True{} : Bool}
  for +cov: {covers(w, h, todo, part) == True{} : Bool}
  for +comp: {completes(w, h, part, layout) == True{} : Bool}
  for +chk: {S.check(S.Ctx{w, h, n, rows, its}, layout) == True{} : Bool}
  for +tok: {todos_ok(todo, layout) == True{} : Bool}
  for +ton: {todos_onb(PS.WH{w, h}, todo) == True{} : Bool}
  for +ion: {items_onb(PS.WH{w, h}, its) == True{} : Bool}
  Empty

Uses (36):
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=cells
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=set_at
  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=and_true_l
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=and_true_r
  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_lists.bend&name=shaped_set
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=check_agree
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=chk_total
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=completes
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=covers
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=dfs_none.node
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=fill_shaped
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=items_onb
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=leaf_agree
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=some_ne_none
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=todos_ok
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=todos_onb
  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=Todo
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=check
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=dfs
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=fill
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=is_none
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=items_ok
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=look
  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=Seen