LAWS.word_or_split: law of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/LAWS.bend as LAWS
Lines 555-563 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=555&end_line=563

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

law word_or_split:
  for +n: Nat
  for +a: Word(n)
  for +b: Word(n)
  for +k: Nat
  for +q: Nat
  for e: {Word.to_nat(n, a) == U.U32Nat.dbl(k, q) : Nat}
  for h: {Nat.is_lt(Word.to_nat(n, b), U.U32Nat.dbl(k, 1n)) == True{} : Bool}
  {Word.to_nat(n, Word.or(n, a, b)) == Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)) : Nat}

Uses (23):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.double
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.or
  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/LAWS.bend&name=nat_add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.double_inj
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt_half
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.odd_even
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.or_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.wc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=ur.r41
  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