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Step * of Lemma pgeo-order_incidence-eq

∀pg:ProjectivePlane. ∀n:ℕ. ∀l1,l2:Line.  (order(pg) = n ⇒ p,q:{p:Point| p I l1} //p ≡ q ~ p,q:{p:Point| p I l2} //p ≡ q\000C)
BY
{ (Auto
   THEN Unfold `pgeo-order` -1
   THEN (InstHyp [⌜l1⌝] (-1)⋅ THENA Auto)
   THEN (InstHyp [⌜l2⌝] (-2)⋅ THENA Auto)
   THEN RelRST
   THEN Auto) }

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Latex:

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Latex:
\mforall{}pg:ProjectivePlane.  \mforall{}n:\mBbbN{}.  \mforall{}l1,l2:Line.
    (order(pg)  =  n  {}\mRightarrow{}  p,q:\{p:Point|  p  I  l1\}  //p  \mequiv{}  q  \msim{}  p,q:\{p:Point|  p  I  l2\}  //p  \mequiv{}  q)


By

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Latex:
(Auto
  THEN  Unfold  `pgeo-order`  -1
  THEN  (InstHyp  [\mkleeneopen{}l1\mkleeneclose{}]  (-1)\mcdot{}  THENA  Auto)
  THEN  (InstHyp  [\mkleeneopen{}l2\mkleeneclose{}]  (-2)\mcdot{}  THENA  Auto)
  THEN  RelRST
  THEN  Auto)

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