def s32

bend-collections-laws-math@1.0.0.0 · proofs/math/random/wrappers.bend:134

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64div.bend as W64D
import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend as PD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend as W64M
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

134def s32(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat) -> {Nat.mul(Nat.mul(x, 65536n), 65536n) == C.shift(32n, x) : Nat}:
135  +k = W64D.k65536(one, h1)
136  +e1 = PD.mul_pow(one, h1, 16n, x, 65536n, k)
137  +e2 = Equal.trans(Nat, Nat.mul(Nat.mul(x, 65536n), 65536n), Nat.mul(WD.sc(16n, x), 65536n), WD.sc(16n, WD.sc(16n, x)), Equal.cong(Nat, Nat, z => Nat.mul(z, 65536n), Nat.mul(x, 65536n), WD.sc(16n, x), e1), PD.mul_pow(one, h1, 16n, WD.sc(16n, x), 65536n, k))
138  Equal.trans(Nat, Nat.mul(Nat.mul(x, 65536n), 65536n), WD.sc(16n, WD.sc(16n, x)), C.shift(32n, x), e2, Equal.trans(Nat, WD.sc(16n, WD.sc(16n, x)), WD.sc(32n, x), C.shift(32n, x), W64M.sc_sc(16n, 16n, x), Equal.sym(Nat, C.shift(32n, x), WD.sc(32n, x), W64M.shift_sc(32n, x))))