def sgv

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64round.bend:330

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/spec/math/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

330def sgv(+one: Nat, +h1: {one == 1n : Nat}, +s: Bool, +c: U32, +hc: {c == U32{WD.pw(32n, 31n)} : U32}) -> {v(SF.pick(U32, s, c, 0)) == C.shift(31n, SF.b2n(s)) : Nat}:
331  Equal.trans(Nat, v(SF.pick(U32, s, c, 0)), C.shift(31n, SF.pick(Nat, s, one, 0n)), C.shift(31n, SF.b2n(s)), sgv0(one, h1, s, c, hc), Equal.cong(Nat, Nat, z => C.shift(31n, z), SF.pick(Nat, s, one, 0n), SF.b2n(s), pb(s, one, h1)))