LAWSDiv.mod_lt: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS_div.bend as LAWSDiv
Lines 17-21 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=17&end_line=21

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

law mod_lt:
  for +a: W.W64
  for +b: W.W64
  for h: {W.W64.is_zero(b) == False{} : Bool}
  {Nat.is_lt(W.W64.to_nat(W.W64.mod(a, b)), W.W64.to_nat(b)) == True{} : Bool}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  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.p2
  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.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