PROOF.li.len_xor: 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 1633-1643 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=1633&end_line=1643

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend as M

def li.len_xor(xs: List<&2, U32>, ys: List<&2, U32>) -> {Nat.is_le(B.len(xs), B.len(ys)) == True{} : Bool} -> {B.len(M.cm.xor_bytes(xs, ys)) == B.len(xs) : Nat}:
  match xs:
    case Nil{}:
      h => {==}
    case Con{+a, +s}:
      match ys:
        case Nil{}:
          h => bo.absurd({B.len(M.cm.xor_bytes(Con{a, s}, Nil{})) == B.len(Con{a, s}) : Nat}, h)
        case Con{+b, +t}:
          h => %li.len_xor(s, t)(h) : {1n+B.len(M.cm.xor_bytes(s, t)) == 1n+_ : Nat}
            {==}

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=bo.absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.xor_bytes