Proof.u64_add_modular: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend as Proof
Lines 43-44 of bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend&start_line=43&end_line=44

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as U
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend as P
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/word_addition.bend as WA
import bend-collections-laws-math@1.0.0.0/spec/math/u64.bend as SU

def u64_add_modular(+a: U.U64, +b: U.U64) -> SU.Add.modular(a, b):
  Equal.trans(Word(64n), P.bits(U.add(a, b)), Word.add(64n, P.bits(a), P.bits(b)), S.from_nat(64n, Nat.add(S.unsigned(64n, P.bits(a)), S.unsigned(64n, P.bits(b)))), P.add(a, b), WA.refines(64n, P.bits(a), P.bits(b)))

Uses (12):
  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.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=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/word_addition.bend&name=refines
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/u64.bend&name=Add.modular
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=add