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Step * of Lemma WCP_wf

∀F:(ℕ+ ⟶ ℤ) ⟶ 𝔹. ∀f:ℕ+ ⟶ ℤ. ∀G:n:ℕ+ ⟶ {g:ℕ+ ⟶ ℤ| f = g ∈ (ℕ+n ⟶ ℤ)} .  (WCP(F;f;G) ∈ {n:ℕ+| F f = F (G n)} )
BY
{ (Intros
   THEN (Assert TERMOF{weak-continuity-principle-nat+-int-bool-ext:o, 1:l}
                ∈ ∀F:(ℕ+ ⟶ ℤ) ⟶ 𝔹. ∀f:ℕ+ ⟶ ℤ. ∀G:n:ℕ+ ⟶ {g:ℕ+ ⟶ ℤ| f = g ∈ (ℕ+n ⟶ ℤ)} .  ∃n:ℕ+. F f = F (G n) BY
               Auto)
   ) }

1
1. F : (ℕ+ ⟶ ℤ) ⟶ 𝔹
2. f : ℕ+ ⟶ ℤ
3. G : n:ℕ+ ⟶ {g:ℕ+ ⟶ ℤ| f = g ∈ (ℕ+n ⟶ ℤ)} 
4. TERMOF{weak-continuity-principle-nat+-int-bool-ext:o, 1:l} ∈ ∀F:(ℕ+ ⟶ ℤ) ⟶ 𝔹. ∀f:ℕ+ ⟶ ℤ. ∀G:n:ℕ+ ⟶ {g:ℕ+ ⟶ ℤ| 
                                                                                                           f
                                                                                                           = g
                                                                                                           ∈ (ℕ+n
                                                                                                             ⟶ ℤ)} .
                                                                  ∃n:ℕ+. F f = F (G n)
⊢ WCP(F;f;G) ∈ {n:ℕ+| F f = F (G n)} 

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Latex:

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Latex:
\mforall{}F:(\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{})  {}\mrightarrow{}  \mBbbB{}.  \mforall{}f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}.  \mforall{}G:n:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \{g:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}|  f  =  g\}  .    (WCP(F;f;G)  \mmember{}  \{n:\mBbbN{}\msupplus{}|  F  f  =  F  (G  n)\}  \000C)


By

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Latex:
(Intros
  THEN  (Assert  TERMOF\{weak-continuity-principle-nat+-int-bool-ext:o,  1:l\}
                            \mmember{}  \mforall{}F:(\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{})  {}\mrightarrow{}  \mBbbB{}.  \mforall{}f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}.  \mforall{}G:n:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \{g:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}|  f  =  g\}  .
                                    \mexists{}n:\mBbbN{}\msupplus{}.  F  f  =  F  (G  n)  BY
                          Auto)
  )

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