AESEnvelopeProof.aes_fixed_bytes_identity: def of qasim-bend-kit@0.1.0.2
Import: import qasim-bend-kit@0.1.0.2/proof/AES_EnvelopeProof.bend as AESEnvelopeProof
Lines 555-580 of qasim-bend-kit@0.1.0.2/proof/AES_EnvelopeProof.bend: https://jend.leeeet.dev/read.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_EnvelopeProof.bend&start_line=555&end_line=580

import Base
import qasim-bend-kit@0.1.0.2/libs/AES256GCM.bend as AES

def aes_fixed_bytes_identity(+n: Nat, +bytes: List<&2, U32>,
    size: {List.length(&2, U32, bytes) == n : Nat}) ->
    {AES.fixed_bytes(n, bytes) == bytes : List<&2, U32>}:
    match n bytes:
        case 0n Nil{}: {==}
        case 0n byte <> tail:
            contradiction = Equal.cong(Nat, Bool,
                x => Nat.is_eq(x, 0n),
                1n+List.length(&2, U32, tail), 0n, size)
            Empty.absurd({AES.fixed_bytes(0n, byte <> tail) ==
                byte <> tail : List<&2, U32>},
                aes_false_true(contradiction))
        case 1n+p Nil{}:
            contradiction = Equal.cong(Nat, Bool,
                x => Nat.is_eq(x, 0n), 0n, 1n+p, size)
            Empty.absurd({AES.fixed_bytes(1n+p, Nil{}) == Nil{} :
                List<&2, U32>},
                aes_false_true(Equal.sym(Bool, True{}, False{},
                    contradiction)))
        case 1n+p byte <> tail:
            tail_size = Equal.cong(Nat, Nat, aes_nat_predecessor,
                1n+List.length(&2, U32, tail), 1n+p, size)
            Equal.cong(List<&2, U32>, List<&2, U32>,
                xs => byte <> xs,
                AES.fixed_bytes(p, tail), tail,
                aes_fixed_bytes_identity(p, tail, tail_size))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  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_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=qasim-bend-kit@0.1.0.2/libs/AES256GCM.bend&name=fixed_bytes
  https://jend.leeeet.dev/definition.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_EnvelopeProof.bend&name=aes_false_true
  https://jend.leeeet.dev/definition.txt?path=qasim-bend-kit@0.1.0.2/proof/AES_EnvelopeProof.bend&name=aes_nat_predecessor