ProofShift.ns.half_le: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 159-169 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=159&end_line=169

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U

# 2 * (x / 2) <= x < 2 + 2 * (x / 2)
def ns.half_le(x: Nat) -> {Nat.is_le(Nat.double(U.U32Nat.half(x)), x) == True{} : Bool}:
  match x:
    case 0n:
      {==}
    case 1n+ +p:
      match p:
        case 0n:
          {==}
        case 1n+ +q:
          ns.half_le(q)

Uses (5):
  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-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.half