LAWS.u32_mod_lt: law of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/LAWS.bend as LAWS
Lines 506-510 of bend-osdev-u32@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&start_line=506&end_line=510

import Base

law u32_mod_lt:
  for +a: U32
  for +b: U32
  for h: {U32.is_zero(b) == False{} : Bool}
  {Nat.is_lt(U32.to_nat(U32.mod(a, b)), U32.to_nat(b)) == True{} : Bool}

Uses (13):
  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=Base/base.bend&name=U32.div.if
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod.if
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.dz
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ud.p2