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Step * of Lemma pgeo-leq_transitivity

∀g:ProjectivePlane. ∀l,m,n:Line.  (l ≡ m ⇒ m ≡ n ⇒ l ≡ n)
BY
{ ((((Auto THEN D 0) THENA Auto) THEN Unfold `pgeo-lsep` -1)
   THEN ExRepD
   THEN (InstLemma`pgeo-leq-preserves-incidence` [⌜g⌝;⌜a⌝;⌜l⌝;⌜m⌝]⋅ THENA EAuto 1)
   THEN (InstLemma`pgeo-leq-preserves-incidence` [⌜g⌝;⌜a⌝;⌜m⌝;⌜n⌝]⋅ THENA EAuto 1)
   THEN D -1
   THEN Auto) }

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Latex:

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Latex:
\mforall{}g:ProjectivePlane.  \mforall{}l,m,n:Line.    (l  \mequiv{}  m  {}\mRightarrow{}  m  \mequiv{}  n  {}\mRightarrow{}  l  \mequiv{}  n)


By

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Latex:
((((Auto  THEN  D  0)  THENA  Auto)  THEN  Unfold  `pgeo-lsep`  -1)
  THEN  ExRepD
  THEN  (InstLemma`pgeo-leq-preserves-incidence`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}l\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{}]\mcdot{}  THENA  EAuto  1)
  THEN  (InstLemma`pgeo-leq-preserves-incidence`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  EAuto  1)
  THEN  D  -1
  THEN  Auto)

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