def aes_fixed_bytes_identity

qasim-bend-kit@0.1.0.2 · proof/AES_EnvelopeProof.bend:555

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

555def aes_fixed_bytes_identity(+n: Nat, +bytes: List<&2, U32>,
556    size: {List.length(&2, U32, bytes) == n : Nat}) ->
557    {AES.fixed_bytes(n, bytes) == bytes : List<&2, U32>}:
558    match n bytes:
559        case 0n Nil{}: {==}
560        case 0n byte <> tail:
561            contradiction = Equal.cong(Nat, Bool,
562                x => Nat.is_eq(x, 0n),
563                1n+List.length(&2, U32, tail), 0n, size)
564            Empty.absurd({AES.fixed_bytes(0n, byte <> tail) ==
565                byte <> tail : List<&2, U32>},
566                aes_false_true(contradiction))
567        case 1n+p Nil{}:
568            contradiction = Equal.cong(Nat, Bool,
569                x => Nat.is_eq(x, 0n), 0n, 1n+p, size)
570            Empty.absurd({AES.fixed_bytes(1n+p, Nil{}) == Nil{} :
571                List<&2, U32>},
572                aes_false_true(Equal.sym(Bool, True{}, False{},
573                    contradiction)))
574        case 1n+p byte <> tail:
575            tail_size = Equal.cong(Nat, Nat, aes_nat_predecessor,
576                1n+List.length(&2, U32, tail), 1n+p, size)
577            Equal.cong(List<&2, U32>, List<&2, U32>,
578                xs => byte <> xs,
579                AES.fixed_bytes(p, tail), tail,
580                aes_fixed_bytes_identity(p, tail, tail_size))