def shrn_div

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/shrn.bend:151

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/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U

151# U32.shrn(x, k) is U32.div(x, 2^k) for k < 32
152def shrn_div(+x: U32, +k: Nat, +hk: {Nat.is_lt(k, 32n) == True{} : Bool}) -> {U32.shrn(x, k) == U32.div(x, X.pow2(k)) : U32}:
153  U.injective(U32.shrn(x, k), U32.div(x, X.pow2(k)), Equal.trans(Nat, v(U32.shrn(x, k)), C.high(k, v(x)), v(U32.div(x, X.pow2(k))), shrn_high(x, k), Equal.sym(Nat, v(U32.div(x, X.pow2(k))), C.high(k, v(x)), div_p2(x, k, hk))))