U64.add_carry: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend as U64
Lines 235-240 of bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend&start_line=235&end_line=240

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend as A
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD

def add_carry(+xw: Word(32n), +c: Bool) -> {U32.add(U32{xw}, U.carry(c)) == U32{WD.incif(32n, c, xw)} : U32}:
  match c:
    case True{}:
      Equal.cong(Word(32n), U32, w => U32{w}, Word.add(32n, xw, WD.one_word(31n)), Word.inc(32n, xw), WD.add_one(31n, xw))
    case False{}:
      A.add_zero(U32{xw})

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.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.inc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=add_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=incif
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=one_word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=carry