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Step * of Lemma filter_is_nil2

∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  filter(P;L) ~ [] supposing (∀x∈L.¬↑P[x])
BY
{ (Auto THEN (InstLemma `filter_is_nil` [⌜{x:T| (x ∈ L)} ⌝]⋅ THENA Auto) THEN BackThruSomeHyp THEN Auto) }

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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{}].    filter(P;L)  \msim{}  []  supposing  (\mforall{}x\mmember{}L.\mneg{}\muparrow{}P[x])


By

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Latex:
(Auto
  THEN  (InstLemma  `filter\_is\_nil`  [\mkleeneopen{}\{x:T|  (x  \mmember{}  L)\}  \mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  BackThruSomeHyp
  THEN  Auto)

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