PROOF.pk.lt_le: def of bend-osdev-pkcs7@0.1.0.0
Import: import bend-osdev-pkcs7@0.1.0.0/PROOF.bend as PROOF
Lines 115-124 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=115&end_line=124

import Base

def pk.lt_le(+x: Nat, +y: Nat) -> {Nat.is_lt(x, 1n+y) == True{} : Bool} -> {Nat.is_le(x, y) == True{} : Bool}:
  match x:
    case 0n:
      h => pk.le0(y)
    case 1n+xp:
      match y:
        case 0n:
          h => pk.absurd({Nat.is_le(1n+xp, 0n) == True{} : Bool}, pk.lt0(xp)(h))
        case 1n+yp:
          h => pk.lt_le(xp, yp)(h)

Uses (7):
  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
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&name=pk.absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&name=pk.le0
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&name=pk.lt0