Step * of Lemma set-valueall-type

[A:Type]. ∀[P:A ⟶ ℙ].  valueall-type({a:A| P[a]} supposing valueall-type(A)
BY
(Auto THEN Using [`B',⌜A⌝(BLemma `subtype-valueall-type`)⋅ THEN Auto) }


Latex:


Latex:
\mforall{}[A:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].    valueall-type(\{a:A|  P[a]\}  )  supposing  valueall-type(A)


By


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




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