Bits.bit_length_le: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/bits.bend as Bits
Lines 112-114 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/bits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/bits.bend&start_line=112&end_line=114

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

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

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/bits.bend&name=le_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=bit_length