Nuprl Lemma : stdEO-causal
∀[M:Type ⟶ Type]
  ∀[S0:InitialSystem(P.M[P])]. ∀[n2m:ℕ ⟶ pMsg(P.M[P])]. ∀[l2m:Id ⟶ pMsg(P.M[P])]. ∀[env:pEnvType(P.M[P])]. ∀[e1,e2:E].
    run-event-step(e1) < run-event-step(e2) supposing (e1 < e2) 
  supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement : 
stdEO: stdEO(n2m;l2m;env;S)
, 
InitialSystem: InitialSystem(P.M[P])
, 
run-event-step: run-event-step(e)
, 
pEnvType: pEnvType(T.M[T])
, 
pMsg: pMsg(P.M[P])
, 
es-causl: (e < e')
, 
es-E: E
, 
Id: Id
, 
strong-type-continuous: Continuous+(T.F[T])
, 
nat: ℕ
, 
less_than: a < b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
eo_axioms: eo_axioms(r)
, 
and: P ∧ Q
, 
stdEO: stdEO(n2m;l2m;env;S)
, 
runEO: runEO(n2m;l2m;env;S)
, 
run-eo: EO(r)
, 
mk-extended-eo: mk-extended-eo, 
top: Top
, 
eq_atom: x =a y
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank)
, 
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank)
, 
btrue: tt
, 
es-causl: (e < e')
, 
es-E: E
, 
assert: ↑b
, 
implies: P 
⇒ Q
Latex:
\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}[S0:InitialSystem(P.M[P])].  \mforall{}[n2m:\mBbbN{}  {}\mrightarrow{}  pMsg(P.M[P])].  \mforall{}[l2m:Id  {}\mrightarrow{}  pMsg(P.M[P])].
    \mforall{}[env:pEnvType(P.M[P])].  \mforall{}[e1,e2:E].
        run-event-step(e1)  <  run-event-step(e2)  supposing  (e1  <  e2) 
    supposing  Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_52_36
Last ObjectModification:
2015_12_29-PM-05_19_23
Theory : process-model
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