ProofGen.gen_inv_wide: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 1173-1181 of minebender-game@1.0.0.0/proof_gen.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_gen.bend&start_line=1173&end_line=1181

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/game.bend as G

# With room for 9 more, n mines fit outside the wider zone.
law gen_inv_wide:
  for +w: Nat
  for +h: Nat
  for +n: Nat
  for +fx: Nat
  for +fy: Nat
  for room: {Nat.is_le(Nat.add(n, 9n), Nat.mul(w, h)) == True{} : Bool}
  {Nat.is_le(n, G.gen.left(G.Zone{T.Pos{fx, fy}, True{}}, B.cells(w, h))) == True{} : Bool}

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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/game.bend&name=Zone
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/game.bend&name=gen.left
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=cells_len
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=gen_left_firsts
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=outs
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=room_left
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=wide_le9
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Pos