Nuprl Lemma : stdEO-event-history
∀[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.
((e1 <loc e2) ⇐⇒ (e1 ∈ run-event-history(pRun(S0;env;n2m;l2m);e2)))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
stdEO: stdEO(n2m;l2m;env;S),
InitialSystem: InitialSystem(P.M[P]),
run-event-history: run-event-history(r;e),
runEvents: runEvents(r),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pMsg: pMsg(P.M[P]),
es-locl: (e <loc e'),
es-E: E,
Id: Id,
l_member: (x ∈ l),
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
stdEO: stdEO(n2m;l2m;env;S),
es-E: E,
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,
assert: ↑b,
InitialSystem: InitialSystem(P.M[P]),
run-event-history: run-event-history(r;e),
let: let,
nat: ℕ,
cand: A c∧ B,
le: A ≤ B,
less_than: a < b,
pi1: fst(t),
pi2: snd(t),
sq_type: SQType(T),
guard: {T},
true: True,
runEvents: runEvents(r),
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
Id: Id,
run-event-loc: run-event-loc(e),
run-event-step: run-event-step(e)
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.
((e1 <loc e2) \mLeftarrow{}{}\mRightarrow{} (e1 \mmember{} run-event-history(pRun(S0;env;n2m;l2m);e2)))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_53_38
Last ObjectModification:
2016_01_18-AM-00_14_04
Theory : process-model
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