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Step * of Lemma assert-bl-all

∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))
BY
{ Assert ⌜∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[L:T List].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))⌝⋅ }

1
.....assertion..... 
∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[L:T List].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))

2
1. ∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[L:T List].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))
⊢ ∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:\{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  \mBbbB{}].    uiff(\muparrow{}(\mforall{}x\mmember{}L.P[x])\_b;(\mforall{}x\mmember{}L.\muparrow{}P[x]))


By

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Latex:
Assert  \mkleeneopen{}\mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[L:T  List].    uiff(\muparrow{}(\mforall{}x\mmember{}L.P[x])\_b;(\mforall{}x\mmember{}L.\muparrow{}P[x]))\mkleeneclose{}\mcdot{}

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