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Step * 1 of Lemma geo-colinear-cons


1. e : BasicGeometry
2. L : Point List
3. A : Point
4. (∀B∈[A / L].(∀C∈[A / L].Colinear(A;B;C)))
5. (∀A@0∈L.(∀B∈[A / L].(∀C∈[A / L].Colinear(A@0;B;C))))
⊢ (∀A∈L.(∀B∈L.(∀C∈L.Colinear(A;B;C))))
BY
{ RepeatFor 2 ((RWO "l_all_cons" (-1) THENA Auto)) }

1
1. e : BasicGeometry
2. L : Point List
3. A : Point
4. (∀B∈[A / L].(∀C∈[A / L].Colinear(A;B;C)))
5. (∀A@0∈L.(Colinear(A@0;A;A) ∧ (∀C∈L.Colinear(A@0;A;C))) ∧ (∀B∈L.Colinear(A@0;B;A) ∧ (∀C∈L.Colinear(A@0;B;C))))
⊢ (∀A∈L.(∀B∈L.(∀C∈L.Colinear(A;B;C))))

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  L  :  Point  List
3.  A  :  Point
4.  (\mforall{}B\mmember{}[A  /  L].(\mforall{}C\mmember{}[A  /  L].Colinear(A;B;C)))
5.  (\mforall{}A@0\mmember{}L.(\mforall{}B\mmember{}[A  /  L].(\mforall{}C\mmember{}[A  /  L].Colinear(A@0;B;C))))
\mvdash{}  (\mforall{}A\mmember{}L.(\mforall{}B\mmember{}L.(\mforall{}C\mmember{}L.Colinear(A;B;C))))


By

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Latex:
RepeatFor  2  ((RWO  "l\_all\_cons"  (-1)  THENA  Auto))

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