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Step * of Lemma Vesley-subset-connected

VesleyAxiom
⇒ (∀P:ℝ ⟶ ℙ
      ((∀x:ℝ. ∀y:{y:ℝ| x = y} .  (P[y] ⇒ P[x])) ⇒ dense-in-interval((-∞, ∞);λx.(¬P[x])) ⇒ Connected({x:ℝ| ¬P[x]} )))
BY
{ (Auto THEN InstLemma `real-subset-connected` [⌜λx.(¬P[x])⌝]⋅ THEN Auto THEN All Reduce THEN Auto) }

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Latex:

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Latex:
VesleyAxiom
{}\mRightarrow{}  (\mforall{}P:\mBbbR{}  {}\mrightarrow{}  \mBbbP{}
            ((\mforall{}x:\mBbbR{}.  \mforall{}y:\{y:\mBbbR{}|  x  =  y\}  .    (P[y]  {}\mRightarrow{}  P[x]))
            {}\mRightarrow{}  dense-in-interval((-\minfty{},  \minfty{});\mlambda{}x.(\mneg{}P[x]))
            {}\mRightarrow{}  Connected(\{x:\mBbbR{}|  \mneg{}P[x]\}  )))


By

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Latex:
(Auto  THEN  InstLemma  `real-subset-connected`  [\mkleeneopen{}\mlambda{}x.(\mneg{}P[x])\mkleeneclose{}]\mcdot{}  THEN  Auto  THEN  All  Reduce  THEN  Auto)

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