PROOF.aria_e13: def of bend-osdev-legacy-ciphers@0.1.0.0
Import: import bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend as PROOF
Lines 8078-8090 of bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend&start_line=8078&end_line=8090

import Base
import bend-osdev-legacy-ciphers@0.1.0.0/aria.bend as A

def aria_e13(s: A.LcAriaSt) -> {s == A.aria.e13(A.aria.e13(s)) : A.LcAriaSt}:
  match s:
    case A.LcAriaSt{+x0, +x1, +x2, +x3, +x4, +x5, +x6, +x7, +x8, +x9, +x10, +x11, +x12, +x13, +x14, +x15}:
      %word_xx(8n, x11, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), Word.xor(8n, Word.xor(8n, x3, x5), x5), Word.xor(8n, Word.xor(8n, x4, x5), x5), x5, x6, x7, Word.xor(8n, Word.xor(8n, x8, x5), x5), Word.xor(8n, Word.xor(8n, x9, x5), x5), Word.xor(8n, Word.xor(8n, x10, x5), x5), _, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x10, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), Word.xor(8n, Word.xor(8n, x3, x5), x5), Word.xor(8n, Word.xor(8n, x4, x5), x5), x5, x6, x7, Word.xor(8n, Word.xor(8n, x8, x5), x5), Word.xor(8n, Word.xor(8n, x9, x5), x5), _, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x9, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), Word.xor(8n, Word.xor(8n, x3, x5), x5), Word.xor(8n, Word.xor(8n, x4, x5), x5), x5, x6, x7, Word.xor(8n, Word.xor(8n, x8, x5), x5), _, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x8, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), Word.xor(8n, Word.xor(8n, x3, x5), x5), Word.xor(8n, Word.xor(8n, x4, x5), x5), x5, x6, x7, _, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x4, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), Word.xor(8n, Word.xor(8n, x3, x5), x5), _, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x3, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), Word.xor(8n, Word.xor(8n, x2, x5), x5), _, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x2, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), Word.xor(8n, Word.xor(8n, x1, x5), x5), _, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x1, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{Word.xor(8n, Word.xor(8n, x0, x5), x5), _, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      %word_xx(8n, x0, x5) : {A.LcAriaSt{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} == A.LcAriaSt{_, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15} : A.LcAriaSt}
      {==}

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.xor
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/PROOF.bend&name=word_xx
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/aria.bend&name=LcAriaSt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-legacy-ciphers@0.1.0.0/aria.bend&name=aria.e13