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Step * of Lemma eu-colinear-from-between

∀e:EuclideanPlane
  ∀[A,C,D:Point].  ((¬(A = C ∈ Point)) ⇒ (∃B:Point. ((¬(A = B ∈ Point)) ∧ A_C_B ∧ A_D_B)) ⇒ Colinear(A;C;D))
BY
{ (Auto THEN ExRepD THEN InstLemma `eu-colinear-between` [⌜e⌝;⌜A⌝;⌜B⌝;⌜C⌝;⌜D⌝]⋅ THEN Auto) }

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Latex:

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Latex:
\mforall{}e:EuclideanPlane
    \mforall{}[A,C,D:Point].    ((\mneg{}(A  =  C))  {}\mRightarrow{}  (\mexists{}B:Point.  ((\mneg{}(A  =  B))  \mwedge{}  A\_C\_B  \mwedge{}  A\_D\_B))  {}\mRightarrow{}  Colinear(A;C;D))


By

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Latex:
(Auto  THEN  ExRepD  THEN  InstLemma  `eu-colinear-between`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}D\mkleeneclose{}]\mcdot{}  THEN  Auto)

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