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def mul_pow

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/poly1305/arith.bend:132

import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as Arith
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/math/typed/width.bend as WW

132# x * 2^k = shift(k, x)
133def mul_pow(+k: Nat, +x: Nat) -> {Nat.mul(x, C.pow2(k)) == C.shift(k, x) : Nat}:
134  tr(Nat.mul(x, C.pow2(k)), Nat.mul(x, C.shift(k, 1n)), C.shift(k, x), Equal.cong(Nat, Nat, t => Nat.mul(x, t), C.pow2(k), C.shift(k, 1n), sy(C.shift(k, 1n), C.pow2(k), WW.shift_one(k))), sy(C.shift(k, x), Nat.mul(x, C.shift(k, 1n)), WW.shift_mul(k, x)))

Uses (9)

Used by (4)