ProofGen.gen_row_count: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 518-530 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=518&end_line=530

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
import minebender-game@1.0.0.0/LAWS.bend as L

law gen_row_count:
  for +z: G.Zone
  for +y: Nat
  for +xs: List<&2, Nat>
  for +st: G.GenState
  for +cs: List<&2, T.Pos>
  for inv: {Nat.is_le(st_need(st), st_left(st)) == True{} : Bool}
  for lft: {st_left(st) == G.gen.left(z, List.append(&2, T.Pos, B.row_cells(y, xs), cs)) : Nat}
  {Nat.add(L.row_mines(G.gen.row(z, y, xs, st)), st_need(G.gen.row_state(z, y, xs, st)))
    == st_need(st) : Nat} &
  {Nat.is_le(st_need(G.gen.row_state(z, y, xs, st)), st_left(G.gen.row_state(z, y, xs, st)))
    == True{} : Bool} &
  {st_left(G.gen.row_state(z, y, xs, st)) == G.gen.left(z, cs) : Nat}

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=List.append
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/LAWS.bend&name=row_mines
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/board.bend&name=row_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=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/game.bend&name=gen.next
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/game.bend&name=gen.row
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/game.bend&name=gen.row_state
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=gen_cell
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=gen_row_count.k
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=st_left
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=st_need
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Pos