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Step * 3 2 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∈L.(∀C∈L.Colinear(A;B;C)))
6. (∀C∈[A / L].Colinear(A;A;C))
⊢ (∀B∈L.(∀C∈[A / L].Colinear(A;B;C)))
BY
{ (Thin (-1) THEN (RWO "l_all_iff" (-1) THENA Auto) THEN (RWO "l_all_iff" 0 THENA Auto)) }

1
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)))

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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\mmember{}L.(\mforall{}C\mmember{}L.Colinear(A;B;C)))
6.  (\mforall{}C\mmember{}[A  /  L].Colinear(A;A;C))
\mvdash{}  (\mforall{}B\mmember{}L.(\mforall{}C\mmember{}[A  /  L].Colinear(A;B;C)))


By

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Latex:
(Thin  (-1)  THEN  (RWO  "l\_all\_iff"  (-1)  THENA  Auto)  THEN  (RWO  "l\_all\_iff"  0  THENA  Auto))

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