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Step * 3 2 1 of Lemma geo-colinear-cons


1. e : BasicGeometry
2. L : Point List
3. A : Point
4. (∀A∈L.(∀B∈L.(∀C∈L.Colinear(A;B;C))))
5. ∀B:Point. ((B ∈ L) ⇒ (∀C∈L.Colinear(A;B;C)))
⊢ ∀B:Point. ((B ∈ L) ⇒ (∀C∈[A / L].Colinear(A;B;C)))
BY
{ (RepeatFor 2 (ParallelLast) THEN Auto) }

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  L  :  Point  List
3.  A  :  Point
4.  (\mforall{}A\mmember{}L.(\mforall{}B\mmember{}L.(\mforall{}C\mmember{}L.Colinear(A;B;C))))
5.  \mforall{}B:Point.  ((B  \mmember{}  L)  {}\mRightarrow{}  (\mforall{}C\mmember{}L.Colinear(A;B;C)))
\mvdash{}  \mforall{}B:Point.  ((B  \mmember{}  L)  {}\mRightarrow{}  (\mforall{}C\mmember{}[A  /  L].Colinear(A;B;C)))


By

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Latex:
(RepeatFor  2  (ParallelLast)  THEN  Auto)

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