ProofValue.wv.gsub.sum: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 486-493 of bend-osdev-word64@0.1.1.0/proof_value.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&start_line=486&end_line=493

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

def wv.gsub.sum(+n: Nat, +ah: Word(n), +al: Word(n), +bh: Word(n), +bl: Word(n)) -> {Nat.add(Nat.add(Word.to_nat(n, Word.sub(n, al, bl)), U.U32Nat.dbl(n, Word.to_nat(n, wv.subhi(n, ah, al, bh, bl)))), wv.V(n, bh, bl)) == Nat.add(wv.V(n, ah, al), wv.Q(n, Nat.add(U.U32Nat.bit(Cmp.is_lt(Word.cmp(n, ah, bh))), U.U32Nat.bit(Cmp.is_lt(Word.cmp(n, Word.sub(n, ah, bh), wv.bitw(n, wv.c1sub(n, al, bl)))))))) : Nat}:
  match n:
    case 0n:
      match ah al bh bl:
        case WNil{} WNil{} WNil{} WNil{}:
          {==}
    case 1n+ +p:
      wv.gsub.go(1n+p, ah, al, bh, bl, wv.bitw_value(p, wv.c1sub(1n+p, al, bl)))

Uses (17):
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  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.sub
  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/u32.bend&name=U32Nat.bit
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.Q
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.V
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.bitw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.bitw_value
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.c1sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.gsub.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wv.subhi