Arith.cadd: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as Arith
Lines 21-23 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&start_line=21&end_line=23

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend as WM

# a + b == a' + b'
def cadd(+a: Nat, +a2: Nat, +b: Nat, +b2: Nat, +ea: {a == a2 : Nat}, +eb: {b == b2 : Nat}) -> {Nat.add(a, b) == Nat.add(a2, b2) : Nat}:
  tr(Nat.add(a, b), Nat.add(a2, b), Nat.add(a2, b2), WM.cong_l(a, a2, b, ea), WM.cong_r(a2, b, b2, eb))

Uses (5):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=tr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend&name=cong_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend&name=cong_r