ProofGen.gen_opening_: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 327-337 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=327&end_line=337

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

# With room, no cell next to the first click gets a mine.
law gen_opening_:
  for +w: Nat
  for +h: Nat
  for +n: Nat
  for +first: T.Pos
  for +rs: List<&2, U32>
  for +room: {Nat.is_le(Nat.add(n, 9n), Nat.mul(w, h)) == True{} : Bool}
  for +q: T.Pos
  for +near: {L.within_one(first, q) == True{} : Bool}
  {L.mine(G.place_mines(w, h, n, first, rs), q) == False{} : Bool}

Uses (18):
  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=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.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=mine
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=within_one
  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_first.row
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=opening_in
  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