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Step * of Lemma Dsep-to-sep

∀e:EuclideanPlane. ∀a,b:Point.  (Dsep(e;a;b) ⇒ a ≠ b)
BY
{ ((Auto THEN Unfold `dist-sep` -1)
   THEN (FLemma `dist-iff-lt` [-1] THEN Auto)
   THEN InstLemma `geo-lt-sep` [⌜e⌝;⌜b⌝;⌜b⌝;⌜a⌝;⌜b⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b:Point.    (Dsep(e;a;b)  {}\mRightarrow{}  a  \mneq{}  b)


By

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Latex:
((Auto  THEN  Unfold  `dist-sep`  -1)
  THEN  (FLemma  `dist-iff-lt`  [-1]  THEN  Auto)
  THEN  InstLemma  `geo-lt-sep`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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