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Step * 1 1 2 of Lemma eu-colinear-trivial


1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. ¬(a = b ∈ Point)@i
5. Colinear(a;b;b)
⇒ ((¬(a = b ∈ Point)) ∧ (¬((¬(b = a ∈ Point)) ∧ (¬(b = b ∈ Point)) ∧ (¬b-a-b) ∧ (¬a-b-b) ∧ (¬a-b-b))))
6. Colinear(a;b;b)
⊢ Colinear(a;b;b)
BY
{ Auto }

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Latex:

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Latex:

1.  e  :  EuclideanPlane@i'
2.  a  :  Point@i
3.  b  :  Point@i
4.  \mneg{}(a  =  b)@i
5.  Colinear(a;b;b)  {}\mRightarrow{}  ((\mneg{}(a  =  b))  \mwedge{}  (\mneg{}((\mneg{}(b  =  a))  \mwedge{}  (\mneg{}(b  =  b))  \mwedge{}  (\mneg{}b-a-b)  \mwedge{}  (\mneg{}a-b-b)  \mwedge{}  (\mneg{}a-b-b))))
6.  Colinear(a;b;b)
\mvdash{}  Colinear(a;b;b)


By

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Latex:
Auto

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