---

Step * 2 of Lemma add-has-value-iff


1. x : partial(ℕ)
2. y : partial(ℕ)
3. (x)↓ ∧ (y)↓
⊢ (x + y)↓
BY
{ ((Assert x ∈ ℕ BY
          (BLemma `termination` THEN Auto))
   THEN (Assert y ∈ ℕ BY
               (BLemma `termination` THEN Auto))
   THEN Auto) }

---

Latex:

---

Latex:

1.  x  :  partial(\mBbbN{})
2.  y  :  partial(\mBbbN{})
3.  (x)\mdownarrow{}  \mwedge{}  (y)\mdownarrow{}
\mvdash{}  (x  +  y)\mdownarrow{}


By

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Latex:
((Assert  x  \mmember{}  \mBbbN{}  BY
                (BLemma  `termination`  THEN  Auto))
  THEN  (Assert  y  \mmember{}  \mBbbN{}  BY
                          (BLemma  `termination`  THEN  Auto))
  THEN  Auto)

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