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Step * 3 2 1 1 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:Point. ((B ∈ L) ⇒ (∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C)))
6. B : Point
7. (B ∈ L)
8. (∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C))
9. ¬(A = B ∈ Point)
⊢ Colinear(A;B;A)
BY
{ EAuto 1 }

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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:Point.  ((B  \mmember{}  L)  {}\mRightarrow{}  (\mforall{}C\mmember{}L.(\mneg{}(A  =  B))  {}\mRightarrow{}  Colinear(A;B;C)))
6.  B  :  Point
7.  (B  \mmember{}  L)
8.  (\mforall{}C\mmember{}L.(\mneg{}(A  =  B))  {}\mRightarrow{}  Colinear(A;B;C))
9.  \mneg{}(A  =  B)
\mvdash{}  Colinear(A;B;A)


By

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Latex:
EAuto  1

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