def dbl53

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64divv.bend:78

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/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

78# 2^53 <= 2 n and n < 2 m for normalized n, m
79def dbl53(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +h: {C.fits(52n, n) == False{} : Bool}) -> {Nat.is_le(C.shift(53n, one), Nat.add(n, n)) == True{} : Bool}:
80  L.subst(Nat, z => {Nat.is_le(C.shift(53n, one), z) == True{} : Bool}, Nat.double(n), Nat.add(n, n), NA.double_self(n), N.double_le(C.shift(52n, one), n, lo52(one, h1, n, h)))