PROOF.un.high_half: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1272-1278 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=1272&end_line=1278

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

# high(k, x / 2) = high(k, x) / 2
def un.high_half(k: Nat, +x: Nat) -> {U.U32Nat.high(k, U.U32Nat.half(x)) == U.U32Nat.half(U.U32Nat.high(k, x)) : Nat}:
  match k:
    case 0n:
      {==}
    case 1n+ +j:
      un.high_half(j, U.U32Nat.half(x))

Uses (3):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.half
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.high