ProofValue.wv.gadd: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 495-502 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=495&end_line=502

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

# W64.add at width n: the sum of the values, less 2^(2n) when it wraps,
# which is when the result is below the first operand
def wv.gadd(+n: Nat, +ah: Word(n), +al: Word(n), +bh: Word(n), +bl: Word(n)) -> {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, U.U32Nat.bit(Nat.is_lt(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.V(n, ah, al))))) == Nat.add(wv.V(n, ah, al), wv.V(n, bh, bl)) : Nat}:
  +ha = wv.val_lt2(n, Word.to_nat(n, al), Word.to_nat(n, ah), UL.word_value_lt(n, al), UL.word_value_lt(n, ah))
  +hb = wv.val_lt2(n, Word.to_nat(n, bl), Word.to_nat(n, bh), UL.word_value_lt(n, bl), UL.word_value_lt(n, bh))
  +ch = wv.char_add(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(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.V(n, ah, al), wv.V(n, bh, bl), wv.gadd.sum(n, ah, al, bh, bl), ha, hb)
  %ch : {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(wv.V(n, ah, al), wv.V(n, bh, bl)) : Nat}
  wv.gadd.sum(n, ah, al, bh, bl)

Uses (17):
  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=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.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_value_lt
  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.char_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.gadd.sum
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.val_lt2