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Step * of Lemma run-pred-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-pred(r) y 
  supposing ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
BY
{ (Auto THEN RepUR ``run-pred`` (-1) THEN D -1 THEN Auto) }

1
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 : runEvents(r)
5. y : runEvents(r)
6. x = (fst(run-info(r;y))) ∈ (ℤ × Id)
⊢ run-event-step(x) < run-event-step(y)

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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-pred(r)  y 
    supposing  \mforall{}e:runEvents(r).  fst(fst(run-info(r;e)))  <  run-event-step(e)


By

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Latex:
(Auto  THEN  RepUR  ``run-pred``  (-1)  THEN  D  -1  THEN  Auto)

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