---

Step * of Lemma tuple-sum_wf

∀[P:Type]. ∀[as:P List]. ∀[G:P ⟶ Type]. ∀[x:tuple-type(map(G;as))]. ∀[f:i:P ⟶ (G i) ⟶ ℕ].  (tuple-sum(f;as;x) ∈ ℕ)
BY
{ (InductionOnList
   THEN Unfold `tuple-sum` 0
   THEN Reduce 0
   THEN ((RWO "null-map" 0 THENA Auto) ORELSE Auto)
   THEN SimpleBoolCase ⌜null(v)⌝⋅
   THEN Auto) }

---

Latex:

---

Latex:
\mforall{}[P:Type].  \mforall{}[as:P  List].  \mforall{}[G:P  {}\mrightarrow{}  Type].  \mforall{}[x:tuple-type(map(G;as))].  \mforall{}[f:i:P  {}\mrightarrow{}  (G  i)  {}\mrightarrow{}  \mBbbN{}].
    (tuple-sum(f;as;x)  \mmember{}  \mBbbN{})


By

---

Latex:
(InductionOnList
  THEN  Unfold  `tuple-sum`  0
  THEN  Reduce  0
  THEN  ((RWO  "null-map"  0  THENA  Auto)  ORELSE  Auto)
  THEN  SimpleBoolCase  \mkleeneopen{}null(v)\mkleeneclose{}\mcdot{}
  THEN  Auto)

---

Home Index