def sh3

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/poly1305/value.bend:326

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/width.bend as WW
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

326# (a + 2^8 b) + 2^8 c == a + 2^8 (b + c)
327def sh3(+a: Nat, +b: Nat, +c: Nat) -> {Nat.add(Nat.add(a, C.shift(8n, b)), C.shift(8n, c)) == Nat.add(a, C.shift(8n, Nat.add(b, c))) : Nat}:
328  A.tr(Nat.add(Nat.add(a, C.shift(8n, b)), C.shift(8n, c)), Nat.add(a, Nat.add(C.shift(8n, b), C.shift(8n, c))), Nat.add(a, C.shift(8n, Nat.add(b, c))),
329    N.add_assoc(a, C.shift(8n, b), C.shift(8n, c)),
330    WM.cong_r(a, Nat.add(C.shift(8n, b), C.shift(8n, c)), C.shift(8n, Nat.add(b, c)), A.sy(C.shift(8n, Nat.add(b, c)), Nat.add(C.shift(8n, b), C.shift(8n, c)), WW.shift_add(8n, b, c))))