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def bit_length_le

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/bits.bend:112

import bend-collections-laws-math@1.0.0.0/proofs/math/natural/bits.bend as Bits
import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M

112# 2^bit_length(n) <= 2 n for n > 0, i.e. 2^(bit_length(n) - 1) <= n   (Mathlib Nat.size_le)
113def bit_length_le(+np: Nat) -> {Nat.is_le(SC.pow2(M.bit_length(1n+np)), Nat.double(1n+np)) == True{} : Bool}:
114  le_go(1n+np, 1n+np, N.le_refl(1n+np))

Uses (8)

Used by (6)