PROOF.rx_comm: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 313-316 of bend-osdev-gf@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&start_line=313&end_line=316

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G

def rx_comm(+a: G.Gf8Bits, +b: G.Gf8Bits) -> {G.Gf8Bits.xor(a, b) == G.Gf8Bits.xor(b, a) : G.Gf8Bits}:
  match a b:
    case G.Gf8Bits{+a0, +a1, +a2, +a3, +a4, +a5, +a6, +a7} G.Gf8Bits{+b0, +b1, +b2, +b3, +b4, +b5, +b6, +b7}:
      rb_eq(Bool.xor(a0, b0), Bool.xor(a1, b1), Bool.xor(a2, b2), Bool.xor(a3, b3), Bool.xor(a4, b4), Bool.xor(a5, b5), Bool.xor(a6, b6), Bool.xor(a7, b7), Bool.xor(b0, a0), Bool.xor(b1, a1), Bool.xor(b2, a2), Bool.xor(b3, a3), Bool.xor(b4, a4), Bool.xor(b5, a5), Bool.xor(b6, a6), Bool.xor(b7, a7), bx_comm(a0, b0), bx_comm(a1, b1), bx_comm(a2, b2), bx_comm(a3, b3), bx_comm(a4, b4), bx_comm(a5, b5), bx_comm(a6, b6), bx_comm(a7, b7))

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.xor
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=bx_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=rb_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.xor