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Step * 1 of Lemma geo-between-out-implies-out


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. c' : Point
6. out(a cc')
7. a-b-c
⊢ out(a c'b)
BY
{ ((Assert out(a bc) BY
          (InstLemma `geo-between-out` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THEN Auto))
   THEN InstLemma `geo-out_transitivity` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜c'⌝]⋅
   THEN EAuto 1) }

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Latex:

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Latex:

1.  e  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  c'  :  Point
6.  out(a  cc')
7.  a-b-c
\mvdash{}  out(a  c'b)


By

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Latex:
((Assert  out(a  bc)  BY
                (InstLemma  `geo-between-out`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto))
  THEN  InstLemma  `geo-out\_transitivity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}c'\mkleeneclose{}]\mcdot{}
  THEN  EAuto  1)

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