AESCertificateProof.nat_decode: def of qasim-bend-kit@0.1.0.2
Import: import qasim-bend-kit@0.1.0.2/proof/AES_CertificateProof.bend as AESCertificateProof
Lines 84-91 of qasim-bend-kit@0.1.0.2/proof/AES_CertificateProof.bend: https://jend.leeeet.dev/read.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_CertificateProof.bend&start_line=84&end_line=91

import Base

def nat_decode(+a: Nat, +b: Nat, code: nat_code(a, b)) -> {a == b : Nat}:
    match a b:
        case 0n 0n: {==}
        case 0n 1n+q: Empty.absurd({a == b : Nat}, code)
        case 1n+p 0n: Empty.absurd({a == b : Nat}, code)
        case 1n+p 1n+q:
            Equal.cong(Nat, Nat, value => 1n+value, p, q,
                nat_decode(p, q, code))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_CertificateProof.bend&name=nat_code