def cancel_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/cong.bend:86

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR

86def cancel_r(+a: Nat, +b: Nat, +c: Nat, +e: {Nat.add(a, c) == Nat.add(b, c) : Nat}) -> {a == b : Nat}:
87  NR.add_cancel(c, a, b, Equal.trans(Nat, Nat.add(c, a), Nat.add(a, c), Nat.add(c, b), NA.add_comm(c, a), Equal.trans(Nat, Nat.add(a, c), Nat.add(b, c), Nat.add(c, b), e, NA.add_comm(b, c))))