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Step * of Lemma remove-first_wf

∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  (remove-first(P;L) ∈ T List)
BY
{ InductionOnList
THEN Unfold `remove-first` 0
THEN Reduce 0
THEN Try (Fold `remove-first` 0)
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{}].    (remove-first(P;L)  \mmember{}  T  List)


By

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Latex:
InductionOnList
THEN  Unfold  `remove-first`  0
THEN  Reduce  0
THEN  Try  (Fold  `remove-first`  0)
THEN  Auto

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