LAWSDiv.divmod_value: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS_div.bend as LAWSDiv
Lines 8-15 of bend-osdev-word64@0.1.1.0/LAWS_div.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/LAWS_div.bend&start_line=8&end_line=15

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

# Division (shift and subtract, 64 steps): for b not 0, the quotient and the
# remainder are the Nat ones, a = q b + r with r < b; by 0, the quotient is 0
# and the remainder a.
law divmod_value:
  for +a: W.W64
  for +b: W.W64
  for h: {W.W64.is_zero(b) == False{} : Bool}
  {Nat.add(Nat.mul(W.W64.to_nat(W.W64.div(a, b)), W.W64.to_nat(b)), W.W64.to_nat(W.W64.mod(a, b))) == W.W64.to_nat(a) : Nat}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wd.dz
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wd.p1
  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.div
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.divmod.pick
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.fst
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.mod
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.snd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat