U32half.hlf_le: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend as U32half
Lines 60-69 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&start_line=60&end_line=69

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

def hlf_le(+n: Nat) -> {Nat.is_le(hlf(n), n) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+p:
      match p:
        case 0n:
          {==}
        case 1n+q:
          N.le_trans(hlf(q), q, 1n+q, hlf_le(q), N.le_succ(q))

Uses (6):
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32half.bend&name=hlf