ProofGen.near_pt.xz: def of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 938-945 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=938&end_line=945

import Base
import minebender-game@1.0.0.0/proof_base.bend as P

def near_pt.xz(+k: Nat) ->
  {Nat.is_le(one(nr(1n+k, 0n)), Nat.add(Nat.add(one(Nat.is_eq(0n, 1n+k)), one(Nat.is_eq(0n, 2n+k))), one(Nat.is_eq(1n, 1n+k))))
    == True{} : Bool}:
  match k:
    case 0n:
      {==}
    case 1n+i:
      P.le_zero_l(Nat.add(Nat.add(one(Nat.is_eq(0n, 2n+i)), one(Nat.is_eq(0n, 3n+i))), one(Nat.is_eq(1n, 2n+i))))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_eq
  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/proof_base.bend&name=le_zero_l
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=nr
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=one