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Step * of Lemma can-find-first2

∀[T:Type]. ∀L:T List. ∀P:{x:T| (x ∈ L)}  ⟶ 𝔹.  ((∃x:T [first-member(T;x;L;P)]) ∨ (∀x∈L.¬↑(P x)))
BY
{ xxx(Auto
      THEN (InstLemma `can-find-first1-ext` [⌜{x:T| (x ∈ L)} ⌝;⌜P⌝;⌜L⌝]⋅ THENA Auto)
      THEN RenameVar `z' (-1)
      THEN UseWitness ⌜z⌝⋅)xxx }

1
1. T : Type
2. L : T List
3. P : {x:T| (x ∈ L)}  ⟶ 𝔹
4. z : (∃x:{x:T| (x ∈ L)}  [first-member({x:T| (x ∈ L)} ;x;L;P)]) ∨ (∀x∈L.¬↑(P x))
⊢ z ∈ (∃x:T [first-member(T;x;L;P)]) ∨ (∀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{}.    ((\mexists{}x:T  [first-member(T;x;L;P)])  \mvee{}  (\mforall{}x\mmember{}L.\mneg{}\muparrow{}(P  x)))


By

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Latex:
xxx(Auto
        THEN  (InstLemma  `can-find-first1-ext`  [\mkleeneopen{}\{x:T|  (x  \mmember{}  L)\}  \mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{}]\mcdot{}  THENA  Auto)
        THEN  RenameVar  `z'  (-1)
        THEN  UseWitness  \mkleeneopen{}z\mkleeneclose{}\mcdot{})xxx

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