def lo52

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64divv.bend:71

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/math/typed/f64round.bend as FR

71# a normalized significand is in [2^52, 2^53)
72def lo52(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +h: {C.fits(52n, n) == False{} : Bool}) -> {Nat.is_le(C.shift(52n, one), n) == True{} : Bool}:
73  N.not_lt_le(n, C.shift(52n, one), Equal.trans(Bool, Nat.is_lt(n, C.shift(52n, one)), C.fits(52n, n), False{}, FR.lt_fit(52n, one, h1, n), h))