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Step * of Lemma geo-colinear-left-out

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∀e:EuclideanPlane. ∀a,b,x,y:Point.  (Colinear(b;x;y) ⇒ x leftof ab ⇒ y leftof ab ⇒ out(b xy))
BY
{ ((Auto THEN ((D 0 THEN Auto) THEN (D 0 THENA Auto)) THEN D -1)
   THEN ((gColinearCases (6) THEN Auto) THEN Try ((EliminatePoint (-1) THEN Auto)))
   THEN (InstLemma `left-between-implies-right1` [⌜e⌝;⌜a⌝;⌜b⌝;⌜x⌝;⌜y⌝]⋅ THEN Auto)
   THEN InstLemma `not-left-and-right` [⌜e⌝;⌜y⌝;⌜a⌝;⌜b⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}e:EuclideanPlane.  \mforall{}a,b,x,y:Point.    (Colinear(b;x;y)  {}\mRightarrow{}  x  leftof  ab  {}\mRightarrow{}  y  leftof  ab  {}\mRightarrow{}  out(b  xy))


By

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Latex:
((Auto  THEN  ((D  0  THEN  Auto)  THEN  (D  0  THENA  Auto))  THEN  D  -1)
  THEN  ((gColinearCases  (6)  THEN  Auto)  THEN  Try  ((EliminatePoint  (-1)  THEN  Auto)))
  THEN  (InstLemma  `left-between-implies-right1`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  InstLemma  `not-left-and-right`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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