LAWSMul.mul_low: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS_mul.bend as LAWSMul
Lines 23-26 of bend-osdev-word64@0.1.1.0/LAWS_mul.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/LAWS_mul.bend&start_line=23&end_line=26

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-word64@0.1.1.0/word64.bend as W

law mul_low:
  for +a: W.W64
  for +b: W.W64
  {W.W64.to_nat(W.W64.mul(a, b)) == U.U32Nat.low(64n, Nat.mul(W.W64.to_nat(a), W.W64.to_nat(b))) : Nat}

Uses (10):
  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=low_unique
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.high
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.low
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/LAWS_mul.bend&name=mul_wrap
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_mul.bend&name=wv.lt64
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat