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Step * 3 1 of Lemma eu-colinear-cons


1. e : EuclideanPlane
2. L : Point List
3. A : Point
4. (∀A∈L.(∀B∈L.(∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C))))
5. (∀B∈L.(∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C)))
⊢ (∀C∈[A / L].(¬(A = A ∈ Point)) ⇒ Colinear(A;A;C))
BY
{ (RWO "l_all_iff" 0 THEN Auto) }

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Latex:

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Latex:

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


By

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Latex:
(RWO  "l\_all\_iff"  0  THEN  Auto)

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