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Step * of Lemma oriented-colinear-trans

∀e:OrientedPlane
  ∀[A,C,B,D:Point].  (Colinear(A;B;C) ⇒ Colinear(B;C;D) ⇒ B ≠ C ⇒ {Colinear(A;C;D) ∧ Colinear(A;B;D)})
BY
{ (InstLemma `geo-colinear-transitivity` [] THEN NthHypSq (-1) THEN EqCD THEN Auto) }

1
1. ∀e:EuclideanPlane
     ∀[A,C,B,D:Point].  (Colinear(A;B;C) ⇒ Colinear(B;C;D) ⇒ B ≠ C ⇒ {Colinear(A;C;D) ∧ Colinear(A;B;D)})
⊢ OrientedPlane ~ EuclideanPlane

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Latex:

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Latex:
\mforall{}e:OrientedPlane
    \mforall{}[A,C,B,D:Point].
        (Colinear(A;B;C)  {}\mRightarrow{}  Colinear(B;C;D)  {}\mRightarrow{}  B  \mneq{}  C  {}\mRightarrow{}  \{Colinear(A;C;D)  \mwedge{}  Colinear(A;B;D)\})


By

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Latex:
(InstLemma  `geo-colinear-transitivity`  []  THEN  NthHypSq  (-1)  THEN  EqCD  THEN  Auto)

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