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Step * 1 of Lemma geo-gt-out-to-between


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. out(a bc)
6. ac > ab
⊢ a_b_c
BY
{ ((InstLemma `geo-gt-implies-lt` [⌜e⌝;⌜a⌝;⌜c⌝;⌜a⌝;⌜b⌝]⋅ THEN Auto)
   THEN ((DoubleNegation THENM SupposeMore (-1)) THENA Auto)
   THEN (RemoveDoubleNegation THENA Auto)
   THEN InstLemma  `geo-lt-out-to-between` [⌜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.  out(a  bc)
6.  ac  >  ab
\mvdash{}  a\_b\_c


By

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Latex:
((InstLemma  `geo-gt-implies-lt`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  ((DoubleNegation  THENM  SupposeMore  (-1))  THENA  Auto)
  THEN  (RemoveDoubleNegation  THENA  Auto)
  THEN  InstLemma    `geo-lt-out-to-between`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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