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


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

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

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Latex:

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Latex:

1.  F  :  (\mBbbN{}  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  \mBbbB{}
\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`  [\mkleeneopen{}F\mkleeneclose{}]\mcdot{}  THENA  Auto)
                THEN  (InstLemma  `uniform-continuity-pi-pi-prop2`  [\mkleeneopen{}\mBbbB{}\mkleeneclose{};\mkleeneopen{}F\mkleeneclose{}]\mcdot{}  THENA  Auto)
                )

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