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Step * of Lemma run-lt-step-less

∀[M:Type ⟶ Type]. ∀[r:pRunType(P.M[P])].
  ∀[x,y:runEvents(r)].  run-event-step(x) < run-event-step(y) supposing x run-lt(r) y 
  supposing ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
BY
{ (InstLemma `run-pred-step-less` []
   THEN RepeatFor 3 (ParallelLast')
   THEN Auto
   THEN RepUR ``run-lt rel_plus`` (-1)
   THEN D -1
   THEN (MoveToConcl (-3) THEN MoveToConcl (-2))
   THEN NatPlusInd (-1)
   THEN Auto
   THEN Try ((RWO "rel_exp_one" (-1) THEN Auto))
   THEN (RWO "rel_exp_iff" (-1) THENM D -1)
   THEN Auto
   THEN ExRepD
   THEN (Assert run-event-step(x) < run-event-step(z) ∧ run-event-step(z) < run-event-step(y) BY
               Auto)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[M:Type  {}\mrightarrow{}  Type].  \mforall{}[r:pRunType(P.M[P])].
    \mforall{}[x,y:runEvents(r)].    run-event-step(x)  <  run-event-step(y)  supposing  x  run-lt(r)  y 
    supposing  \mforall{}e:runEvents(r).  fst(fst(run-info(r;e)))  <  run-event-step(e)


By

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Latex:
(InstLemma  `run-pred-step-less`  []
  THEN  RepeatFor  3  (ParallelLast')
  THEN  Auto
  THEN  RepUR  ``run-lt  rel\_plus``  (-1)
  THEN  D  -1
  THEN  (MoveToConcl  (-3)  THEN  MoveToConcl  (-2))
  THEN  NatPlusInd  (-1)
  THEN  Auto
  THEN  Try  ((RWO  "rel\_exp\_one"  (-1)  THEN  Auto))
  THEN  (RWO  "rel\_exp\_iff"  (-1)  THENM  D  -1)
  THEN  Auto
  THEN  ExRepD
  THEN  (Assert  run-event-step(x)  <  run-event-step(z)  \mwedge{}  run-event-step(z)  <  run-event-step(y)  BY
                          Auto)
  THEN  Auto)

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