Float.bl_le: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend as Float
Lines 144-156 of bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&start_line=144&end_line=156

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/src/math/natural.bend as M
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/w64clz.bend as WC

def bl_le(+k: Nat, +n: Nat, +h: {C.fits(k, n) == True{} : Bool}) -> {Nat.is_le(M.bit_length(n), k) == True{} : Bool}:
  match k:
    case 0n:
      +en = N.eq_from_is_eq(n, 0n, h)
      %Equal.sym(Nat, n, 0n, en) : {Nat.is_le(M.bit_length(_), 0n) == True{} : Bool}
      {==}
    case 1n+ +kp:
      match n:
        case 0n:
          {==}
        case 1n+ +np:
          %Equal.sym(Nat, M.bit_length(1n+np), 1n+M.bit_length(C.half(1n+np)), WC.bl_succ(np)) : {Nat.is_le(_, 1n+kp) == True{} : Bool}
          bl_le(kp, C.half(1n+np), h)

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=eq_from_is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64clz.bend&name=bl_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=half
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=bit_length