PROOFText.wr.t1: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 107-111 of bend-osdev-word64@0.1.1.0/PROOF_text.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&start_line=107&end_line=111

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def wr.t1(+x0: Nat, +x1: Nat, +x2: Nat) -> {Nat.add(Nat.mul(x0, x1), Nat.mul(x2, x1)) == Nat.mul(Nat.add(x0, x2), x1) : Nat}:
  %Equal.sym(Nat, Nat.mul(x2, x1), Nat.mul(x1, x2), UL.nat_mul_comm(x2, x1)) : {Nat.add(Nat.mul(x0, x1), _) == Nat.mul(Nat.add(x0, x2), x1) : Nat}
  %Equal.sym(Nat, Nat.mul(x1, x2), Nat.mul(x2, x1), Equal.sym(Nat, Nat.mul(x2, x1), Nat.mul(x1, x2), UL.nat_mul_comm(x2, x1))) : {Nat.add(Nat.mul(x0, x1), _) == Nat.mul(Nat.add(x0, x2), x1) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.mul(x0, x1), Nat.mul(x2, x1)), Nat.mul(Nat.add(x0, x2), x1), Equal.sym(Nat, Nat.mul(Nat.add(x0, x2), x1), Nat.add(Nat.mul(x0, x1), Nat.mul(x2, x1)), UL.nat_add_mul(x0, x2, x1))) : {_ == Nat.mul(Nat.add(x0, x2), x1) : Nat}
  {==}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_mul_comm