def rot

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/poly1305/step.bend:48

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend as WM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A

48# a + (b + c) == (a + c) + b
49def rot(+a: Nat, +b: Nat, +c: Nat) -> {Nat.add(a, Nat.add(b, c)) == Nat.add(Nat.add(a, c), b) : Nat}:
50  A.tr(Nat.add(a, Nat.add(b, c)), Nat.add(a, Nat.add(c, b)), Nat.add(Nat.add(a, c), b), WM.cong_r(a, Nat.add(b, c), Nat.add(c, b), N.add_comm(b, c)), A.sy(Nat.add(Nat.add(a, c), b), Nat.add(a, Nat.add(c, b)), N.add_assoc(a, c, b)))