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


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

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

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Latex:

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Latex:

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


By

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

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