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Step * of Lemma geo-colinear-is-colinear-set

No Annotations
∀e:EuclideanPlane. ∀A,B,C:Point.  (Colinear(A;B;C) ⇒ geo-colinear-set(e; [A; B; C]))
BY
{ ((Auto
    THEN (Assert BasicGeometryAxioms(e) BY
                (D 1 THEN Unhide THEN Auto))
    THEN (InstLemma  `geo-axioms-imply` [⌜e⌝]⋅ THENA Auto)
    THEN ExRepD)
   THEN (D 0 THENA Auto)
   THEN (Reduce -1 THEN IntSegCases (-1))
   THEN Reduce 0
   THEN RepeatFor 2 (ProveLAll)
   THEN (D 0 THEN Auto)
   THEN FLemma  `lsep-implies-sep` [-1]
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}e:EuclideanPlane.  \mforall{}A,B,C:Point.    (Colinear(A;B;C)  {}\mRightarrow{}  geo-colinear-set(e;  [A;  B;  C]))


By

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Latex:
((Auto
    THEN  (Assert  BasicGeometryAxioms(e)  BY
                            (D  1  THEN  Unhide  THEN  Auto))
    THEN  (InstLemma    `geo-axioms-imply`  [\mkleeneopen{}e\mkleeneclose{}]\mcdot{}  THENA  Auto)
    THEN  ExRepD)
  THEN  (D  0  THENA  Auto)
  THEN  (Reduce  -1  THEN  IntSegCases  (-1))
  THEN  Reduce  0
  THEN  RepeatFor  2  (ProveLAll)
  THEN  (D  0  THEN  Auto)
  THEN  FLemma    `lsep-implies-sep`  [-1]
  THEN  Auto)

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