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Step * 1 of Lemma strong-continuity2-implies-uniform-continuity2-int


1. F : (ℕ ⟶ 𝔹) ⟶ ℤ
⊢ ∃n:ℕ. ∀f,g:ℕ ⟶ 𝔹.  ((f = g ∈ (ℕn ⟶ 𝔹)) ⇒ ((F f) = (F g) ∈ ℤ))
BY
{ TACTIC:((InstLemma `strong-continuity2-implies-uniform-continuity-int-ext` [⌜F⌝]⋅ THENA Auto)
          THEN (InstLemma `uniform-continuity-pi-pi-prop2` [⌜ℤ⌝;⌜F⌝]⋅ THENA Auto)
          ) }

1
1. F : (ℕ ⟶ 𝔹) ⟶ ℤ
2. ⇃(∃n:ℕ. ∀f,g:ℕ ⟶ 𝔹.  ((f = g ∈ (ℕn ⟶ 𝔹)) ⇒ ((F f) = (F g) ∈ ℤ)))
3. ∃n:ℕ. ucpB(ℤ;F;n) ⇐⇒ ∃n:ℕ. ucA(ℤ;F;n)
⊢ ∃n:ℕ. ∀f,g:ℕ ⟶ 𝔹.  ((f = g ∈ (ℕn ⟶ 𝔹)) ⇒ ((F f) = (F g) ∈ ℤ))

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Latex:

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Latex:

1.  F  :  (\mBbbN{}  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  \mBbbZ{}
\mvdash{}  \mexists{}n:\mBbbN{}.  \mforall{}f,g:\mBbbN{}  {}\mrightarrow{}  \mBbbB{}.    ((f  =  g)  {}\mRightarrow{}  ((F  f)  =  (F  g)))


By

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Latex:
TACTIC:((InstLemma  `strong-continuity2-implies-uniform-continuity-int-ext`  [\mkleeneopen{}F\mkleeneclose{}]\mcdot{}  THENA  Auto)
                THEN  (InstLemma  `uniform-continuity-pi-pi-prop2`  [\mkleeneopen{}\mBbbZ{}\mkleeneclose{};\mkleeneopen{}F\mkleeneclose{}]\mcdot{}  THENA  Auto)
                )

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