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Step * 1 of Lemma Dbet-iff-between


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. ∀A,B,C:Point.  (A # BC ⇒ |AC| < |AB| + |BC|)
6. Dbet(e;a;b;c)
⊢ a_b_c
BY
{ (InstLemma `Dbet-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.  \mforall{}A,B,C:Point.    (A  \#  BC  {}\mRightarrow{}  |AC|  <  |AB|  +  |BC|)
6.  Dbet(e;a;b;c)
\mvdash{}  a\_b\_c


By

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Latex:
(InstLemma  `Dbet-to-between`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto)

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