def pwv

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/f64bits.bend:58

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/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD

58# the value of a constant c = 2^k
59def pwv(+k: Nat, +hk: {Nat.is_lt(k, 32n) == True{} : Bool}, +one: Nat, +h1: {one == 1n : Nat}, +c: U32, +hc: {c == U32{WD.pw(32n, k)} : U32}) -> {v(c) == C.shift(k, one) : Nat}:
60  +e0 = Equal.trans(Nat, v(U32{WD.pw(32n, k)}), S.unsigned(32n, WD.pw(32n, k)), C.shift(k, one), U.to_nat_word(WD.pw(32n, k)), Equal.trans(Nat, S.unsigned(32n, WD.pw(32n, k)), S.scale_binary(k, one), C.shift(k, one), WD.pwv(32n, k, hk, one, h1, WD.pw(32n, k), {==}), sb(k, one)))
61  L.subst(U32, z => {v(z) == C.shift(k, one) : Nat}, U32{WD.pw(32n, k)}, c, Equal.sym(U32, c, U32{WD.pw(32n, k)}, hc), e0)