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Step * 4 of Lemma eu-eq_dist-axiomsB


1. g : EuclideanPlane
2. ∀a,b,c:Point.  (a # bc ⇒ |ac| < |ab| + |bc|)
3. a : Point
4. b : Point
5. c : Point
6. Dbet(g;a;b;c)
7. Dsep(g;b;c)
⊢ D(a;c;c;c;a;b)
BY
{ ((InstLemma `Dbet-to-between` [⌜g⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THEN Auto)
   THEN (FLemma `Dsep-to-sep` [-2] THEN Auto)
   THEN Unfold `dist` 0
   THEN InstConcl [⌜a⌝;⌜c⌝;⌜c⌝;⌜b⌝]⋅
   THEN Auto) }

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Latex:

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Latex:

1.  g  :  EuclideanPlane
2.  \mforall{}a,b,c:Point.    (a  \#  bc  {}\mRightarrow{}  |ac|  <  |ab|  +  |bc|)
3.  a  :  Point
4.  b  :  Point
5.  c  :  Point
6.  Dbet(g;a;b;c)
7.  Dsep(g;b;c)
\mvdash{}  D(a;c;c;c;a;b)


By

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Latex:
((InstLemma  `Dbet-to-between`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  (FLemma  `Dsep-to-sep`  [-2]  THEN  Auto)
  THEN  Unfold  `dist`  0
  THEN  InstConcl  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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