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Step * of Lemma geo-colinear-out-cases

∀[e:BasicGeometry-]. ∀[a,b,c:Point].  ∀X:ℙ. (Stable{X} ⇒ Colinear(a;b;c) ⇒ (out(a bc) ⇒ X) ⇒ (c_a_b ⇒ X) ⇒ X)
BY
{ (InstLemma `geo-simple-colinear-cases` []
   THEN RepeatFor 7 ((ParallelLast' THENA Auto))
   THEN Auto
   THEN StableCases ⌜out(a bc)⌝⋅
   THEN Auto
   THEN FLemma `geo-colinear-not-out` [-1]
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[e:BasicGeometry-].  \mforall{}[a,b,c:Point].
    \mforall{}X:\mBbbP{}.  (Stable\{X\}  {}\mRightarrow{}  Colinear(a;b;c)  {}\mRightarrow{}  (out(a  bc)  {}\mRightarrow{}  X)  {}\mRightarrow{}  (c\_a\_b  {}\mRightarrow{}  X)  {}\mRightarrow{}  X)


By

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Latex:
(InstLemma  `geo-simple-colinear-cases`  []
  THEN  RepeatFor  7  ((ParallelLast'  THENA  Auto))
  THEN  Auto
  THEN  StableCases  \mkleeneopen{}out(a  bc)\mkleeneclose{}\mcdot{}
  THEN  Auto
  THEN  FLemma  `geo-colinear-not-out`  [-1]
  THEN  Auto)

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