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Step * of Lemma geo-lt-add1_1

∀e:BasicGeometry. ∀p,q,r:Length.  (p < q ⇒ p < q + r)
BY
{ (((Auto THEN Unfold `geo-lt` -1 THEN ExRepD) THEN Unfold `geo-lt` 0 THEN InstConcl [⌜a⌝;⌜b⌝]⋅ THEN Auto)
   THEN (Assert q ≤ q + r BY
               (InstLemma `geo-le-add1` [⌜e⌝;⌜q⌝;⌜r⌝]⋅ THEN Auto))
   THEN InstLemma `geo-le_transitivity` [⌜e⌝;⌜p + |ab|⌝;⌜q⌝;⌜q + r⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}e:BasicGeometry.  \mforall{}p,q,r:Length.    (p  <  q  {}\mRightarrow{}  p  <  q  +  r)


By

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Latex:
(((Auto  THEN  Unfold  `geo-lt`  -1  THEN  ExRepD)
    THEN  Unfold  `geo-lt`  0
    THEN  InstConcl  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
    THEN  Auto)
  THEN  (Assert  q  \mleq{}  q  +  r  BY
                          (InstLemma  `geo-le-add1`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}q\mkleeneclose{};\mkleeneopen{}r\mkleeneclose{}]\mcdot{}  THEN  Auto))
  THEN  InstLemma  `geo-le\_transitivity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}p  +  |ab|\mkleeneclose{};\mkleeneopen{}q\mkleeneclose{};\mkleeneopen{}q  +  r\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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