Word.add_exact: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as Word
Lines 59-61 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&start_line=59&end_line=61

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/addition_bounds.bend as AB

# addition below 2^n is exact
def add_exact(+n: Nat, +one: Nat, +h1: {one == 1n : Nat}, +a: Word(n), +b: Word(n), +h: {Nat.is_lt(Nat.add(uw(n, a), uw(n, b)), sc(n, one)) == True{} : Bool}) -> {uw(n, Word.add(n, a, b)) == Nat.add(uw(n, a), uw(n, b)) : Nat}:
  AB.exact(n, a, b, lt1(n, one, h1, Nat.add(uw(n, a), uw(n, b)), h))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/addition_bounds.bend&name=exact
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=lt1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=uw