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Step * of Lemma CLK_strict_inc2

∀MsgType:ValueAllType. ∀f:CLK_headers_type{i:l}(MsgType). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀clock1,clock2:ℤ.
  ((∃e:E. ((e1 <loc e) ∧ e ≤loc e2  ∧ (↑e ∈b CLK_msg'base(MsgType;f))))
  ⇒ (e1 <loc e2)
  ⇒ clock1 ∈ CLK_Clock(MsgType;f)(e1)
  ⇒ clock2 ∈ CLK_Clock(MsgType;f)(e2)
  ⇒ clock1 < clock2)
BY
{ (Auto
   THEN ExRepD
   THEN (RWO "assert-member-eclass" (-4) THENA Auto)
   THEN TrySquashExRepD (-4)
   THEN InstLemma `CLK_stric_inc` [⌈MsgType⌉;⌈f⌉;⌈es⌉;⌈e1⌉;⌈e2⌉;⌈clock1⌉;⌈clock2⌉]⋅
   THEN Auto
   THEN InstConcl [⌈v⌉;⌈e⌉]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}MsgType:ValueAllType.  \mforall{}f:CLK\_headers\_type\{i:l\}(MsgType).  \mforall{}es:EO+(Message(f)).  \mforall{}e1,e2:E.
\mforall{}clock1,clock2:\mBbbZ{}.
    ((\mexists{}e:E.  ((e1  <loc  e)  \mwedge{}  e  \mleq{}loc  e2    \mwedge{}  (\muparrow{}e  \mmember{}\msubb{}  CLK\_msg'base(MsgType;f))))
    {}\mRightarrow{}  (e1  <loc  e2)
    {}\mRightarrow{}  clock1  \mmember{}  CLK\_Clock(MsgType;f)(e1)
    {}\mRightarrow{}  clock2  \mmember{}  CLK\_Clock(MsgType;f)(e2)
    {}\mRightarrow{}  clock1  <  clock2)


By

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Latex:
(Auto
  THEN  ExRepD
  THEN  (RWO  "assert-member-eclass"  (-4)  THENA  Auto)
  THEN  TrySquashExRepD  (-4)
  THEN  InstLemma  `CLK\_stric\_inc`  [\mkleeneopen{}MsgType\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e1\mkleeneclose{};\mkleeneopen{}e2\mkleeneclose{};\mkleeneopen{}clock1\mkleeneclose{};\mkleeneopen{}clock2\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  InstConcl  [\mkleeneopen{}v\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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