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Step * 1 2 2 2 of Lemma geo-colinear-implies


1. e : BasicGeometry-
2. BasicGeometryAxioms(e)
3. a : Point
4. b : Point
5. c : Point
6. ¬a # bc
7. ¬(((¬ab>ac) ∧ (¬bc>ac)) ∧ (¬a # bc))
8. ∀a,b,c,d:Point.  (ab>cd ⇒ (¬cd>ab))
9. bc>ac
10. ¬ca>cb
11. ab>cb
12. ¬bc>ba
13. ca>ba
⊢ False
BY
{ ((InstLemma  `geo-gt-prim-transitivity` [⌜e⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜c⌝;⌜b⌝;⌜a⌝]⋅ THEN Auto)
   THENA (InstLemma  `geo-gt-prim-symmetry` [⌜e⌝;⌜c⌝;⌜a⌝;⌜b⌝;⌜a⌝]⋅ THEN Auto)
   ) }

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Latex:

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Latex:

1.  e  :  BasicGeometry-
2.  BasicGeometryAxioms(e)
3.  a  :  Point
4.  b  :  Point
5.  c  :  Point
6.  \mneg{}a  \#  bc
7.  \mneg{}(((\mneg{}ab>ac)  \mwedge{}  (\mneg{}bc>ac))  \mwedge{}  (\mneg{}a  \#  bc))
8.  \mforall{}a,b,c,d:Point.    (ab>cd  {}\mRightarrow{}  (\mneg{}cd>ab))
9.  bc>ac
10.  \mneg{}ca>cb
11.  ab>cb
12.  \mneg{}bc>ba
13.  ca>ba
\mvdash{}  False


By

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Latex:
((InstLemma    `geo-gt-prim-transitivity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THENA  (InstLemma    `geo-gt-prim-symmetry`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}  THEN  Auto)
  )

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