ProofGen.gen_count_: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 1217-1225 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=1217&end_line=1225

import Base
import minebender-game@1.0.0.0/types.bend as T
import minebender-game@1.0.0.0/game.bend as G
import minebender-game@1.0.0.0/LAWS.bend as L

law gen_count_:
  for +w: Nat
  for +h: Nat
  for +n: Nat
  for +first: T.Pos
  for +rs: List<&2, U32>
  for on: {L.on_board(w, h, first) == True{} : Bool}
  for fits: {Nat.is_lt(n, Nat.mul(w, h)) == True{} : Bool}
  {L.total_mines(G.place_mines(w, h, n, first, rs)) == n : Nat}

Uses (17):
  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=List.range
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=on_board
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=total_mines
  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=GenState
  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/game.bend&name=place_mines
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=gen_inv
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=gen_rows_count
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=zone
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Pos