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
Lemmas :
rec_select_update_lemma,
pRun_wf2,
pRunType_wf,
Id_wf,
run-event-loc_wf,
less_than_wf,
run-event-step_wf,
nat_wf,
member-mapfilter,
le_wf,
from-upto_wf,
l_member_wf,
set_wf,
is-run-event_wf,
subtype_rel_sets,
assert_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
run-event-history_wf,
true_wf,
runEvents_wf,
zero-le-nat,
member-from-upto,
atom2_subtype_base,
sq_stable__assert,
set_subtype_base,
product_subtype_base,
int_subtype_base,
es-locl_wf,
stdEO_wf,
event-ordering+_subtype,
pMsg_wf,
pRun_wf,
fulpRunType-subtype,
iff_wf
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:
2015_07_23-AM-11_16_35
Last ObjectModification:
2015_01_28-PM-11_19_57
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