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Step * 3 of Lemma run-eo_wf


1. M : Type ─→ Type
2. r : pRunType(P.M[P])
3. ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
4. ∀x,y:runEvents(r).  ((↓x run-lt(r) y) ⇒ run-event-step(x) < run-event-step(y))
5. ∀e:runEvents(r). (run-event-loc(run_local_pred(r;e)) = run-event-loc(e) ∈ Id)
6. e : runEvents(r)@i
⊢ ¬↓e run-lt(r) run_local_pred(r;e)
BY
{ ((D 0 THEN Auto)
   THEN (FLemma `run-lt-step-less` [-1] THENA Auto)
   THEN (InstLemma `run_local_pred_time` [⌈M⌉;⌈r⌉;⌈e⌉]⋅ THENA Auto)
   THEN Fold `run-event-step` (-1)
   THEN Auto') }

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Latex:

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Latex:

1.  M  :  Type  {}\mrightarrow{}  Type
2.  r  :  pRunType(P.M[P])
3.  \mforall{}e:runEvents(r).  fst(fst(run-info(r;e)))  <  run-event-step(e)
4.  \mforall{}x,y:runEvents(r).    ((\mdownarrow{}x  run-lt(r)  y)  {}\mRightarrow{}  run-event-step(x)  <  run-event-step(y))
5.  \mforall{}e:runEvents(r).  (run-event-loc(run\_local\_pred(r;e))  =  run-event-loc(e))
6.  e  :  runEvents(r)@i
\mvdash{}  \mneg{}\mdownarrow{}e  run-lt(r)  run\_local\_pred(r;e)


By

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Latex:
((D  0  THEN  Auto)
  THEN  (FLemma  `run-lt-step-less`  [-1]  THENA  Auto)
  THEN  (InstLemma  `run\_local\_pred\_time`  [\mkleeneopen{}M\mkleeneclose{};\mkleeneopen{}r\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Fold  `run-event-step`  (-1)
  THEN  Auto')

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