PROOF.na.lt_le: def of bend-osdev-cipher-modes@0.1.0.0
Import: import bend-osdev-cipher-modes@0.1.0.0/PROOF.bend as PROOF
Lines 292-301 of bend-osdev-cipher-modes@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&start_line=292&end_line=301

import Base

def na.lt_le(+a: Nat, +b: Nat) -> {Nat.is_lt(a, b) == True{} : Bool} -> {Nat.is_le(a, b) == True{} : Bool}:
  match a b:
    case 0n 0n:
      h => bo.absurd({Nat.is_le(0n, 0n) == True{} : Bool}, h)
    case 0n 1n+bp:
      h => {==}
    case 1n+ap 0n:
      h => bo.absurd({Nat.is_le(1n+ap, 0n) == True{} : Bool}, h)
    case 1n+ap 1n+bp:
      h => na.lt_le(ap, bp)(h)

Uses (5):
  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-cipher-modes@0.1.0.0/PROOF.bend&name=bo.absurd