---

Step * of Lemma isect-valueall-type

∀[A:Type]. ∀[B:A ⟶ Type].  ((∃a:A. valueall-type(B[a])) ⇒ valueall-type(⋂a:A. B[a]))
BY
{ (Auto THEN D -1 THEN Using [`B',⌜B[a]⌝] (BLemma `subtype-valueall-type`)⋅ THEN Auto) }

---

Latex:

---

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].    ((\mexists{}a:A.  valueall-type(B[a]))  {}\mRightarrow{}  valueall-type(\mcap{}a:A.  B[a]))


By

---

Latex:
(Auto  THEN  D  -1  THEN  Using  [`B',\mkleeneopen{}B[a]\mkleeneclose{}]  (BLemma  `subtype-valueall-type`)\mcdot{}  THEN  Auto)

---

Home Index