def bl_nfit

bend-collections-laws-math@1.0.0.0 · proofs/math/random/fround.bend:307

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/width.bend as WW
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend as FO

307def bl_nfit(+n: Nat, +hz: {Nat.is_eq(n, 0n) == False{} : Bool}) -> {C.fits(Nat.sub(M.bit_length(n), 1n), n) == False{} : Bool}:
308  +K = Nat.sub(M.bit_length(n), 1n)
309  +nf = Equal.trans(Bool, C.fits(K, C.pow2(K)), Nat.is_lt(C.pow2(K), C.pow2(K)), False{}, WW.fits_lt(K, C.pow2(K)), N.lt_irrefl(C.pow2(K)))
310  nfit(K, C.pow2(K), n, FO.lower(n, hz), nf)