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Step * 1 of Lemma find-first_wf


1. T : Type
2. L : T List
3. P : {x:T| (x ∈ L)}  ⟶ 𝔹
⊢ TERMOF{can-find-first-ext:o, 1:l, 1:l} L P ∈ (∃x:T [first-member(T;x;L;P)]) ∨ (∀x∈L.¬↑(P x))
BY
{ Subst' TERMOF{can-find-first-ext:o, 1:l, 1:l} ~ TERMOF{can-find-first-ext:o, i:l, i:l} 0⋅ }

1
.....equality..... 
1. T : Type
2. L : T List
3. P : {x:T| (x ∈ L)}  ⟶ 𝔹
⊢ TERMOF{can-find-first-ext:o, 1:l, 1:l} ~ TERMOF{can-find-first-ext:o, i:l, i:l}

2
1. T : Type
2. L : T List
3. P : {x:T| (x ∈ L)}  ⟶ 𝔹
⊢ TERMOF{can-find-first-ext:o, i:l, i:l} L P ∈ (∃x:T [first-member(T;x;L;P)]) ∨ (∀x∈L.¬↑(P x))

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Latex:

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Latex:

1.  T  :  Type
2.  L  :  T  List
3.  P  :  \{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  \mBbbB{}
\mvdash{}  TERMOF\{can-find-first-ext:o,  1:l,  1:l\}  L  P  \mmember{}  (\mexists{}x:T  [first-member(T;x;L;P)])  \mvee{}  (\mforall{}x\mmember{}L.\mneg{}\muparrow{}(P  x))


By

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Latex:
Subst'  TERMOF\{can-find-first-ext:o,  1:l,  1:l\}  \msim{}  TERMOF\{can-find-first-ext:o,  i:l,  i:l\}  0\mcdot{}

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