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Step * of Lemma geo-between-outer-trans-cpy

∀e:EuclideanPlane. ∀[a,b,c,d:Point].  (a_c_d) supposing (b_c_d and a_b_c and b ≠ c)
BY
{ (Auto
   THEN (gSeparatedCases ⌜a⌝ ⌜c⌝⋅ THEN Auto)
   THEN ((InstLemma `extend-using-SC` [⌜e⌝;⌜a⌝;⌜c⌝;⌜d⌝]⋅ THENA Auto) THEN ExRepD)
   THEN (InstLemma `geo-construction-unicity2` [⌜e⌝;⌜b⌝;⌜c⌝;⌜x⌝;⌜d⌝]⋅ THEN EAuto 1)
   THEN RWO "-1" (-3)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d:Point].    (a\_c\_d)  supposing  (b\_c\_d  and  a\_b\_c  and  b  \mneq{}  c)


By

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Latex:
(Auto
  THEN  (gSeparatedCases  \mkleeneopen{}a\mkleeneclose{}  \mkleeneopen{}c\mkleeneclose{}\mcdot{}  THEN  Auto)
  THEN  ((InstLemma  `extend-using-SC`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}  THENA  Auto)  THEN  ExRepD)
  THEN  (InstLemma  `geo-construction-unicity2`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}  THEN  EAuto  1)
  THEN  RWO  "-1"  (-3)
  THEN  Auto)

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