ProofSpeed.dfs2_eq: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_speed.bend as ProofSpeed
Lines 506-522 of minebender-game@1.0.0.0/proof_speed.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_speed.bend&start_line=506&end_line=522

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

# With the counts right and every cell on the board, the counting search
# answers exactly as the plain one.
law dfs2_eq:
  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 +t: Nat
  for +f: Nat
  for +sh: {B.shaped(Maybe<&2, Bool>, w, h, part) == True{} : Bool}
  for +con: {tall(~PS.WH, ~con_f, PS.WH{w, h}, todo) == True{} : Bool}
  for +et: {S.part_true(part) == t : Nat}
  for +ef: {S.part_none(part) == f : Nat}
  {S.dfs2(todo, part, t, f, S.Ctx{w, h, n, rows, its}) == S.dfs(todo, part, S.Ctx{w, h, n, rows, its}) : Maybe<&2, T.Grid(Bool)>}

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=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=Base/base.bend&name=Nat.sub
  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_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_speed.bend&name=con_f
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_speed.bend&name=dfs2_eq.node
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_speed.bend&name=tall
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_speed.bend&name=tall_head
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_speed.bend&name=tall_tail
  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=dfs
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=dfs2
  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=look
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=part_none
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/solver.bend&name=part_true
  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