PROOF.pk.le_step: def of bend-osdev-pkcs7@0.1.0.0
Import: import bend-osdev-pkcs7@0.1.0.0/PROOF.bend as PROOF
Lines 58-65 of bend-osdev-pkcs7@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&start_line=58&end_line=65

import Base

def pk.le_step(+x: Nat, +y: Nat) -> {Nat.is_le(x, y) == True{} : Bool} -> {Nat.is_le(x, 1n+y) == True{} : Bool}:
  match x y:
    case 0n _:
      h => {==}
    case 1n+xp 0n:
      h => pk.absurd({Nat.is_le(1n+xp, 1n) == True{} : Bool}, h)
    case 1n+xp 1n+yp:
      h => pk.le_step(xp, yp)(h)

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=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&name=pk.absurd