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Step * 2 of Lemma Dtri-iff-lsep


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. a # bc
⊢ Dtri(e;a;b;c)
BY
{ ((InstLemma `Euclid-Prop20_cycle` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THEN Auto)
   THEN Unfold `dist-tri` 0
   THEN (InstLemma `dist-iff-lt` [⌜e⌝;⌜a⌝;⌜b⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜c⌝]⋅ THENA Auto)
   THEN (InstLemma `dist-iff-lt` [⌜e⌝;⌜a⌝;⌜c⌝;⌜a⌝;⌜b⌝;⌜b⌝;⌜c⌝]⋅ THENA Auto)
   THEN InstLemma `dist-iff-lt` [⌜e⌝;⌜a⌝;⌜c⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜b⌝]⋅
   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.  a  \#  bc
\mvdash{}  Dtri(e;a;b;c)


By

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Latex:
((InstLemma  `Euclid-Prop20\_cycle`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  Unfold  `dist-tri`  0
  THEN  (InstLemma  `dist-iff-lt`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (InstLemma  `dist-iff-lt`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  InstLemma  `dist-iff-lt`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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