PROOF.AP.shln_pw: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 384-391 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=384&end_line=391

import Base

# shln(1, d) is 2^d
def AP.shln_pw(d: Nat) -> {U32.shln(1, d) == U32{AP.pw(32n, d)} : U32}:
  match d:
    case 0n:
      {==}
    case 1n+ +e:
      %Equal.sym(U32, U32.shln(1, e), U32{AP.pw(32n, e)}, AP.shln_pw(e)) : {U32.shl(_) == U32{AP.pw(32n, 1n+e)} : U32}
      AP.u32_cong(Word.shl(32n, AP.pw(32n, e)), AP.pw(32n, 1n+e), Equal.trans(Word(32n), Word.shl(32n, AP.pw(32n, e)), Word.shl.put(32n, False{}, AP.pw(32n, e)), AP.pw(32n, 1n+e), AP.shl_put(32n, AP.pw(32n, e)), AP.sp(32n, e)))

Uses (14):
  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=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl.put
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.pw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.shl_put
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.sp
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.u32_cong