LAWSMul.mulhi_value: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS_mul.bend as LAWSMul
Lines 8-16 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=8&end_line=16

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

# Multiplication. W64.mulhi(a, b) is the high 32 bits of the product of two
# 32-bit words: with the low 32 bits (U32.mul), the whole product. W64.mul
# is the product modulo 2^64: its value is the low 64 bits of the product of
# the values (U32Nat.low, from bend-osdev-u32), what wraps is 2^64 times the
# rest, and with the product no more than a word's value nothing wraps.
law mulhi_value:
  for +a: U32
  for +b: U32
  {Nat.add(U32.to_nat(U32.mul(a, b)), U.U32Nat.dbl(32n, U32.to_nat(W.W64.mulhi(a, b)))) == Nat.mul(U32.to_nat(a), U32.to_nat(b)) : Nat}

Uses (19):
  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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_add_wrap
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_and_65535
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_mul_low
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_shrn_value
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_mul.bend&name=wm.k
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_mul.bend&name=wu.lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.mulhi