ProofSolver.among_lo: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_solver.bend as ProofSolver
Lines 259-267 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=259&end_line=267

import Base
import minebender-game@1.0.0.0/types.bend as T
import minebender-game@1.0.0.0/proof_cells.bend as PS
import minebender-game@1.0.0.0/proof_sums.bend as PU

law among_lo:
  for +w: Nat
  for +h: Nat
  for +part: T.Grid(Maybe<&2, Bool>)
  for +layout: T.Grid(Bool)
  for +comp: {completes(w, h, part, layout) == True{} : Bool}
  for +ps: List<&2, T.Pos>
  for +ons: {PS.allp(~PS.WH, ~PS.onb, PS.WH{w, h}, ps) == True{} : Bool}
  {Nat.is_le(PU.csum(~Maybe<&2, Bool>, ~tf, None{}, part, ps), PU.csum(~Bool, ~one, False{}, layout, ps)) == True{} : Bool}

Uses (21):
  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.is_le
  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/proof_base.bend&name=le_add
  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=cell_lo
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=comp_cell
  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=one
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_solver.bend&name=tf
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_sums.bend&name=csum
  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=Pos