ProofValue.wv.gadd.go: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 466-470 of bend-osdev-word64@0.1.1.0/proof_value.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&start_line=466&end_line=470

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

# the value of the sum of two words of two halves, with its carry out
def wv.gadd.go(+n: Nat, +ah: Word(n), +al: Word(n), +bh: Word(n), +bl: Word(n), eb: {Word.to_nat(n, wv.bitw(n, wv.c1add(n, al, bl))) == U.U32Nat.bit(wv.c1add(n, al, bl)) : Nat}) -> {Nat.add(Nat.add(Word.to_nat(n, Word.add(n, al, bl)), U.U32Nat.dbl(n, Word.to_nat(n, wv.addhi(n, ah, al, bh, bl)))), wv.Q(n, Nat.add(U.U32Nat.bit(Cmp.is_lt(Word.cmp(n, Word.add(n, ah, bh), ah))), U.U32Nat.bit(Cmp.is_lt(Word.cmp(n, wv.addhi(n, ah, al, bh, bl), Word.add(n, ah, bh))))))) == Nat.add(wv.V(n, ah, al), wv.V(n, bh, bl)) : Nat}:
  +tw = Word.add(n, ah, bh)
  +bw = wv.bitw(n, wv.c1add(n, al, bl))
  wv.nadd(n, wv.c1add(n, al, bl), Cmp.is_lt(Word.cmp(n, tw, ah)), Cmp.is_lt(Word.cmp(n, wv.addhi(n, ah, al, bh, bl), tw)), Word.to_nat(n, Word.add(n, al, bl)), Word.to_nat(n, tw), Word.to_nat(n, wv.addhi(n, ah, al, bh, bl)), Word.to_nat(n, al), Word.to_nat(n, ah), Word.to_nat(n, bl), Word.to_nat(n, bh), Word.to_nat(n, bw), UL.word_add_wrap(n, al, bl), UL.word_add_wrap(n, ah, bh), UL.word_add_wrap(n, tw, bw), eb)

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_lt
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp
  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=word_add_wrap
  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/proof_value.bend&name=wv.Q
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.V
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.addhi
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.bitw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.c1add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.nadd