PROOF.AP.le_succ: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 70-83 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=70&end_line=83

import Base

def AP.le_succ(y: Nat, x: Nat) -> {Nat.is_le(1n+y, x) == Nat.is_lt(y, x) : Bool}:
  match y x:
    case 0n 0n:
      {==}
    case 0n 1n+p:
      match p:
        case 0n:
          {==}
        case 1n+q:
          {==}
    case 1n+q 0n:
      {==}
    case 1n+q 1n+p:
      AP.le_succ(q, p)

Uses (4):
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt