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Step * 2 1 of Lemma eu-colinear-cons


1. e : EuclideanPlane
2. L : Point List
3. A : Point
4. (((¬(A = A ∈ Point)) ⇒ Colinear(A;A;A)) ∧ (∀C∈L.(¬(A = A ∈ Point)) ⇒ Colinear(A;A;C)))
∧ (∀B∈L.((¬(A = B ∈ Point)) ⇒ Colinear(A;B;A)) ∧ (∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C)))
⊢ (∀B∈L.(∀C∈L.(¬(A = B ∈ Point)) ⇒ Colinear(A;B;C)))
BY
{ (D -1 THEN (RWO "l_all_iff" (-1) THENA Auto) THEN (RWO "l_all_iff" 0 THENA Auto) THEN ParallelLast THEN Auto) }

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Latex:

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Latex:

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


By

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

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