PROOF.bitw.popcount_le: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 160-169 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=160&end_line=169

import Base
import bend-osdev-algo@0.1.0.0/algo.bend as A

def bitw.popcount_le(n: Nat, w: Word(n)) -> {Nat.is_le(A.bitw.popcount(n, w), n) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+ +p:
      match w:
        case WCon{True{}, t}:
          bitw.popcount_le(p, t)
        case WCon{False{}, +t}:
          nat.le_succ(A.bitw.popcount(p, t), p, bitw.popcount_le(p, t))

Uses (7):
  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=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=nat.le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bitw.popcount