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Step * of Lemma geo-colinear-implies-between-or

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∀e:EuclideanPlane. ∀a,b,c:Point.  (Colinear(a;b;c) ⇒ (¬¬((B(acb) ∨ B(bac)) ∨ B(abc))))
BY
{ (Auto
   THEN (Unfold `geo-colinear` -1 THEN Unfold `geo-lsep` -1)
   THEN (Assert (¬a leftof bc) ∧ (¬a leftof cb) BY
               Auto)
   THEN InstLemma  `not-left-collinear` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
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\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    (Colinear(a;b;c)  {}\mRightarrow{}  (\mneg{}\mneg{}((B(acb)  \mvee{}  B(bac))  \mvee{}  B(abc))))


By

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Latex:
(Auto
  THEN  (Unfold  `geo-colinear`  -1  THEN  Unfold  `geo-lsep`  -1)
  THEN  (Assert  (\mneg{}a  leftof  bc)  \mwedge{}  (\mneg{}a  leftof  cb)  BY
                          Auto)
  THEN  InstLemma    `not-left-collinear`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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