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Step * of Lemma strong-continuity2-implies-weak-skolem

∀F:(ℕ ⟶ ℕ) ⟶ ℕ. ⇃(∃M:(ℕ ⟶ ℕ) ⟶ ℕ. ∀f,g:ℕ ⟶ ℕ.  ((f = g ∈ (ℕM f ⟶ ℕ)) ⇒ ((F f) = (F g) ∈ ℕ)))
BY
{ ((UnivCD THENA Auto)
   THEN (Assert ⇃(strong-continuity2(ℕ;F)) BY
               ((InstLemma `strong-continuity2-no-inner-squash` [⌜F⌝]⋅ THENA Auto)
                THEN Unfold `strong-continuity2` 0
                THEN Auto))
   THEN Fold `weak-continuity-skolem` 0
   THEN MoveToConcl (-1)
   THEN BLemma  `implies-quotient-true`
   THEN Auto) }

1
1. F : (ℕ ⟶ ℕ) ⟶ ℕ
2. strong-continuity2(ℕ;F)
⊢ weak-continuity-skolem(ℕ;F)

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Latex:

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Latex:
\mforall{}F:(\mBbbN{}  {}\mrightarrow{}  \mBbbN{})  {}\mrightarrow{}  \mBbbN{}.  \00D9(\mexists{}M:(\mBbbN{}  {}\mrightarrow{}  \mBbbN{})  {}\mrightarrow{}  \mBbbN{}.  \mforall{}f,g:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}.    ((f  =  g)  {}\mRightarrow{}  ((F  f)  =  (F  g))))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (Assert  \00D9(strong-continuity2(\mBbbN{};F))  BY
                          ((InstLemma  `strong-continuity2-no-inner-squash`  [\mkleeneopen{}F\mkleeneclose{}]\mcdot{}  THENA  Auto)
                            THEN  Unfold  `strong-continuity2`  0
                            THEN  Auto))
  THEN  Fold  `weak-continuity-skolem`  0
  THEN  MoveToConcl  (-1)
  THEN  BLemma    `implies-quotient-true`
  THEN  Auto)

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