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Step * of Lemma eu-segments-cross

∀e:EuclideanPlane. ∀p,b,q,a:Point.  ((∃c:Point. ((¬Colinear(a;b;c)) ∧ a-p-c ∧ b_q_c)) ⇒ (∃x:Point. (p-x-b ∧ q-x-a)))
BY
{ (Auto THEN ExRepD THEN InstLemma `eu-inner-pasch-property` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜p⌝;⌜q⌝]⋅ THEN Auto) }

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Latex:

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Latex:
\mforall{}e:EuclideanPlane.  \mforall{}p,b,q,a:Point.
    ((\mexists{}c:Point.  ((\mneg{}Colinear(a;b;c))  \mwedge{}  a-p-c  \mwedge{}  b\_q\_c))  {}\mRightarrow{}  (\mexists{}x:Point.  (p-x-b  \mwedge{}  q-x-a)))


By

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Latex:
(Auto  THEN  ExRepD  THEN  InstLemma  `eu-inner-pasch-property`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{};\mkleeneopen{}q\mkleeneclose{}]\mcdot{}  THEN  Auto)

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