PROOF.um.k: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1373-1382 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=1373&end_line=1382

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

def um.k(+n: Nat, m: Nat, a: Word(m), +b: Word(n), +acc: Word(n)) -> Nat:
  match m:
    case 0n:
      0n
    case 1n+ +mp:
      match a:
        case WCon{False{}, +at}:
          Nat.add(um.k(n, mp, at, Word.shl(n, b), acc), Nat.mul(Word.to_nat(mp, at), U.U32Nat.bit(un.top(n, b))))
        case WCon{True{}, +at}:
          Nat.add(um.k(n, mp, at, Word.shl(n, b), Word.add(n, acc, b)), Nat.add(U.U32Nat.bit(Cmp.is_lt(Word.cmp(n, Word.add(n, acc, b), acc))), Nat.mul(Word.to_nat(mp, at), U.U32Nat.bit(un.top(n, b)))))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=Base/base.bend&name=Word.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp
  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.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.top
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit