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Step * of Lemma decidable-finite-cantor-to-int

∀[R:ℤ ⟶ ℤ ⟶ ℙ]. ((∀x,y:ℤ.  Dec(R[x;y])) ⇒ (∀n:ℕ. ∀F:(ℕn ⟶ 𝔹) ⟶ ℤ.  Dec(∃f,g:ℕn ⟶ 𝔹. R[F f;F g])))
BY
{ (Auto THEN RenameVar `dcdr' 2 THEN UseWitness ⌜finite-cantor-decider(dcdr;n;F)⌝⋅ THEN Auto) }

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Latex:

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Latex:
\mforall{}[R:\mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}  {}\mrightarrow{}  \mBbbP{}]
    ((\mforall{}x,y:\mBbbZ{}.    Dec(R[x;y]))  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  \mforall{}F:(\mBbbN{}n  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  \mBbbZ{}.    Dec(\mexists{}f,g:\mBbbN{}n  {}\mrightarrow{}  \mBbbB{}.  R[F  f;F  g])))


By

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Latex:
(Auto  THEN  RenameVar  `dcdr'  2  THEN  UseWitness  \mkleeneopen{}finite-cantor-decider(dcdr;n;F)\mkleeneclose{}\mcdot{}  THEN  Auto)

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