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Step * of Lemma runEO_wf

∀[M:Type ⟶ Type]
  ∀[n2m:ℕ ⟶ pMsg(P.M[P])]. ∀[l2m:Id ⟶ pMsg(P.M[P])]. ∀[S0:System(P.M[P])]. ∀[env:pEnvType(P.M[P])].
    runEO(n2m;l2m;env;S0) ∈ EO+(pMsg(P.M[P])) supposing run-initialization(pRun(S0;env;n2m;l2m);snd(S0)) 
  supposing Continuous+(P.M[P])
BY
{ (BasicUniformUnivCD Auto
   THEN (Assert pRun(S0;env;n2m;l2m) ∈ pRunType(P.M[P]) BY
               (DoSubsume THEN Auto))
   THEN (ProveWfLemma THEN BLemma `run-initialization-property`⋅ THEN Auto)⋅) }

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Latex:

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Latex:
\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}[n2m:\mBbbN{}  {}\mrightarrow{}  pMsg(P.M[P])].  \mforall{}[l2m:Id  {}\mrightarrow{}  pMsg(P.M[P])].  \mforall{}[S0:System(P.M[P])].
    \mforall{}[env:pEnvType(P.M[P])].
        runEO(n2m;l2m;env;S0)  \mmember{}  EO+(pMsg(P.M[P])) 
        supposing  run-initialization(pRun(S0;env;n2m;l2m);snd(S0)) 
    supposing  Continuous+(P.M[P])


By

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Latex:
(BasicUniformUnivCD  Auto
  THEN  (Assert  pRun(S0;env;n2m;l2m)  \mmember{}  pRunType(P.M[P])  BY
                          (DoSubsume  THEN  Auto))
  THEN  (ProveWfLemma  THEN  BLemma  `run-initialization-property`\mcdot{}  THEN  Auto)\mcdot{})

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