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Step * 1 of Lemma geo-lt_functionality_wrt_implies


1. e : BasicGeometry
2. a : Length
3. b : Length
4. c : Length
5. d : Length
6. geo_ge(e; b; a)
7. c ≤ d
8. b < c
⊢ a < d
BY
{ ((InstLemma `geo-lt_transitivity` [⌜e⌝;⌜a⌝;⌜b⌝;⌜d⌝]⋅ THEN Auto)
   THEN InstLemma `geo-lt_transitivity2` [⌜e⌝;⌜b⌝;⌜c⌝;⌜d⌝]⋅
   THEN Auto) }

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  a  :  Length
3.  b  :  Length
4.  c  :  Length
5.  d  :  Length
6.  geo\_ge(e;  b;  a)
7.  c  \mleq{}  d
8.  b  <  c
\mvdash{}  a  <  d


By

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Latex:
((InstLemma  `geo-lt\_transitivity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  InstLemma  `geo-lt\_transitivity2`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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