LAWS.sub_wrap: law of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/LAWS.bend as LAWS
Lines 140-146 of bend-osdev-word64@0.1.1.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/LAWS.bend&start_line=140&end_line=146

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-word64@0.1.1.0/word64.bend as W

# Subtraction, for every pair of words: the difference plus the subtrahend
# is the minuend, plus 2^64 when the subtrahend is the larger; when it is
# not, the difference is the Nat difference.
law sub_wrap:
  for +a: W.W64
  for +b: W.W64
  {Nat.add(W.W64.to_nat(W.W64.sub(a, b)), W.W64.to_nat(b)) == Nat.add(W.W64.to_nat(a), U.U32Nat.dbl(64n, U.U32Nat.bit(W.W64.is_lt(a, b)))) : Nat}

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.sub
  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
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/LAWS.bend&name=lt_value
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF.bend&name=wp.sub_split
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.gsub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.subhi
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat