LAWSBits.and_or: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS_bits.bend as LAWSBits
Lines 25-28 of bend-osdev-word64@0.1.1.0/LAWS_bits.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/LAWS_bits.bend&start_line=25&end_line=28

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

law and_or:
  for +a: W.W64
  for +b: W.W64
  {Nat.add(W.W64.to_nat(W.W64.and(a, b)), W.W64.to_nat(W.W64.or(a, b))) == Nat.add(W.W64.to_nat(a), W.W64.to_nat(b)) : Nat}

Uses (15):
  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.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=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.or
  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_and_or
  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_bits.bend&name=wr.b0
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_bits.bend&name=wr.b1
  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.and
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.or
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat