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Step * of Lemma geo-not-triangle

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∀e:HeytingGeometry. ∀a,b,c:Point.  ((¬a # bc) ⇒ (¬((¬B(abc)) ∧ (¬B(bca)) ∧ (¬B(cab)))))
BY
{ (Auto THEN InstLemma  `geo-colinear-implies-between-or` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THEN Auto) }

1
1. e : HeytingGeometry
2. a : Point
3. b : Point
4. c : Point
5. ¬a # bc
6. ¬¬((B(acb) ∨ B(bac)) ∨ B(abc))
⊢ ¬((¬B(abc)) ∧ (¬B(bca)) ∧ (¬B(cab)))

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Latex:

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Latex:
No  Annotations
\mforall{}e:HeytingGeometry.  \mforall{}a,b,c:Point.    ((\mneg{}a  \#  bc)  {}\mRightarrow{}  (\mneg{}((\mneg{}B(abc))  \mwedge{}  (\mneg{}B(bca))  \mwedge{}  (\mneg{}B(cab)))))


By

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Latex:
(Auto  THEN  InstLemma    `geo-colinear-implies-between-or`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto)

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