PROOFText.wr.t0: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 101-105 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=101&end_line=105

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

def wr.t0(+x0: Nat, +x1: Nat) -> {Nat.mul(x0, U.U32Nat.dbl(x1, 1n)) == U.U32Nat.dbl(x1, x0) : Nat}:
  %Equal.sym(Nat, Nat.mul(x0, U.U32Nat.dbl(x1, 1n)), U.U32Nat.dbl(x1, Nat.mul(x0, 1n)), UL.dbl_mul_r(x1, x0, 1n)) : {_ == U.U32Nat.dbl(x1, x0) : Nat}
  %Equal.sym(Nat, Nat.mul(x0, 1n), Nat.mul(1n, x0), UL.nat_mul_comm(x0, 1n)) : {U.U32Nat.dbl(x1, _) == U.U32Nat.dbl(x1, x0) : Nat}
  %Equal.sym(Nat, Nat.mul(1n, x0), x0, UL.nat_one_mul(x0)) : {U.U32Nat.dbl(x1, _) == U.U32Nat.dbl(x1, x0) : Nat}
  {==}

Uses (7):
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_mul_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl