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Step * of Lemma Process-apply_wf

∀[M:Type ⟶ Type]
  ∀[P:Process(P.M[P])]. ∀[m:pMsg(P.M[P])].  (Process-apply(P;m) ∈ Process(P.M[P]) × pExt(P.M[P])) 
  supposing Continuous+(P.M[P])
BY
{ ((ProveWfLemma THEN GenConclAtAddrType ⌜pMsg(P.M[P]) ⟶ (Process(P.M[P]) × pExt(P.M[P]))⌝ [2;1]⋅)
   THEN Auto
   THEN DoSubsume
   THEN Auto) }

1
1. M : Type ⟶ Type
2. Continuous+(P.M[P])
3. P : Process(P.M[P])
4. m : pMsg(P.M[P])
5. P = P ∈ Process(P.M[P])
⊢ Process(P.M[P]) ⊆r (pMsg(P.M[P]) ⟶ (Process(P.M[P]) × pExt(P.M[P])))

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Latex:

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Latex:
\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}[P:Process(P.M[P])].  \mforall{}[m:pMsg(P.M[P])].    (Process-apply(P;m)  \mmember{}  Process(P.M[P])  \mtimes{}  pExt(P.M[P])) 
    supposing  Continuous+(P.M[P])


By

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Latex:
((ProveWfLemma  THEN  GenConclAtAddrType  \mkleeneopen{}pMsg(P.M[P])  {}\mrightarrow{}  (Process(P.M[P])  \mtimes{}  pExt(P.M[P]))\mkleeneclose{}  [2;1]\mcdot{})
  THEN  Auto
  THEN  DoSubsume
  THEN  Auto)

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