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Step * 1 of Lemma Dtri-iff-lsep


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. Dtri(e;a;b;c)
⊢ a # bc
BY
{ (((Unfold `dist-tri` -1 THEN ExRepD) THEN RepeatFor 3 ((FLemma `dist-iff-lt` [-3] THEN Auto)))
   THEN InstLemma `Prop22-inequality-implies-triangle` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅
   THEN Auto) }

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Latex:

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Latex:

1.  e  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  Dtri(e;a;b;c)
\mvdash{}  a  \#  bc


By

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Latex:
(((Unfold  `dist-tri`  -1  THEN  ExRepD)  THEN  RepeatFor  3  ((FLemma  `dist-iff-lt`  [-3]  THEN  Auto)))
  THEN  InstLemma  `Prop22-inequality-implies-triangle`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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