PROOFMul.wr.m3: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_mul.bend as PROOFMul
Lines 151-154 of bend-osdev-word64@0.1.1.0/PROOF_mul.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_mul.bend&start_line=151&end_line=154

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.m3(+x0: Nat) -> {Nat.mul(U.U32Nat.dbl(x0, 1n), U.U32Nat.dbl(x0, 1n)) == U.U32Nat.dbl(x0, U.U32Nat.dbl(x0, 1n)) : Nat}:
  %Equal.sym(Nat, Nat.mul(U.U32Nat.dbl(x0, 1n), U.U32Nat.dbl(x0, 1n)), U.U32Nat.dbl(x0, Nat.mul(1n, U.U32Nat.dbl(x0, 1n))), UL.dbl_mul_l(x0, 1n, U.U32Nat.dbl(x0, 1n))) : {_ == U.U32Nat.dbl(x0, U.U32Nat.dbl(x0, 1n)) : Nat}
  %Equal.sym(Nat, Nat.mul(1n, U.U32Nat.dbl(x0, 1n)), U.U32Nat.dbl(x0, Nat.mul(1n, 1n)), UL.dbl_mul_r(x0, 1n, 1n)) : {U.U32Nat.dbl(x0, _) == U.U32Nat.dbl(x0, U.U32Nat.dbl(x0, 1n)) : 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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_mul_l
  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/u32.bend&name=U32Nat.dbl