Nuprl Lemma : stdEO-le
∀[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 ⇐⇒ (run-event-loc(e1) = run-event-loc(e2) ∈ Id) ∧ (run-event-step(e1) ≤ run-event-step(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),
run-event-loc: run-event-loc(e),
pEnvType: pEnvType(T.M[T]),
pMsg: pMsg(P.M[P]),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
stdEO-locl,
nat_wf,
stdEO-eq-E,
es-E_wf,
stdEO_wf,
event-ordering+_subtype,
pMsg_wf,
pEnvType_wf,
Id_wf,
InitialSystem_wf,
strong-type-continuous_wf,
es-locl_wf,
equal_wf,
rec_select_update_lemma,
run-event-loc_wf,
pRun_wf2,
run-event-step_wf,
le_weakening2,
le_weakening,
or_wf,
le_wf,
iff_wf,
less_than_wf,
decidable__equal_int,
decidable__lt,
false_wf,
not-equal-2,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
add-associates
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 \mleq{}loc e2
\mLeftarrow{}{}\mRightarrow{} (run-event-loc(e1) = run-event-loc(e2)) \mwedge{} (run-event-step(e1) \mleq{} run-event-step(e2)))
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_16_30
Last ObjectModification:
2015_01_28-PM-11_19_27
Home
Index