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Step * 1 of Lemma member_filter_2


1. [T] : Type
⊢ ∀P:{x:T| (x ∈ [])}  ⟶ 𝔹. ∀x:T.  ((x ∈ filter(P;[])) ⇐⇒ (x ∈ []) ∧ (↑(P x)))
BY
{ (Reduce 0 THEN Auto) }

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Latex:

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Latex:

1.  [T]  :  Type
\mvdash{}  \mforall{}P:\{x:T|  (x  \mmember{}  [])\}    {}\mrightarrow{}  \mBbbB{}.  \mforall{}x:T.    ((x  \mmember{}  filter(P;[]))  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  [])  \mwedge{}  (\muparrow{}(P  x)))


By

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Latex:
(Reduce  0  THEN  Auto)

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