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Step * 4 1 of Lemma dual-plane_wf


1. pg : ProjectivePlaneStructureComplete
2. BasicProjectiveGeometryAxioms(pg)
3. triangle-axiom1(pg)
4. triangle-axiom2(pg)
5. BasicProjectiveGeometryAxioms(dual-plane(pg))
6. triangle-axiom1(dual-plane(pg))
⊢ ∀p,q:Line. ∀l,m:Point. ∀s:p ≠ q. ∀s1:l ≠ m.
    (pgeo-plsep(pg; l; p) ⇒ pgeo-plsep(pg; m; q) ⇒ m I p ⇒ l I q ⇒ pgeo-plsep(pg; p ∧ q; l ∨ m))
BY
{ (InstLemma `pgeo-triangle-axiom2-dual` [⌜pg⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  pg  :  ProjectivePlaneStructureComplete
2.  BasicProjectiveGeometryAxioms(pg)
3.  triangle-axiom1(pg)
4.  triangle-axiom2(pg)
5.  BasicProjectiveGeometryAxioms(dual-plane(pg))
6.  triangle-axiom1(dual-plane(pg))
\mvdash{}  \mforall{}p,q:Line.  \mforall{}l,m:Point.  \mforall{}s:p  \mneq{}  q.  \mforall{}s1:l  \mneq{}  m.
        (pgeo-plsep(pg;  l;  p)  {}\mRightarrow{}  pgeo-plsep(pg;  m;  q)  {}\mRightarrow{}  m  I  p  {}\mRightarrow{}  l  I  q  {}\mRightarrow{}  pgeo-plsep(pg;  p  \mwedge{}  q;  l  \mvee{}  m))


By

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Latex:
(InstLemma  `pgeo-triangle-axiom2-dual`  [\mkleeneopen{}pg\mkleeneclose{}]\mcdot{}  THEN  Auto)

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