PROOF.na.add_sub: 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 280-290 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=280&end_line=290

import Base

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

Uses (6):
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=bo.absurd