Nuprl Lemma : CLK-ilf
∀[MsgType:{T:Type| valueall-type(T)} ]. ∀[locs:bag(Id)]. ∀[reply:Id ─→ MsgType ─→ (MsgType × Id)].
∀[f:CLK_headers_type{i:l}(MsgType)]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(f)].
{<d, i, m> ∈ CLK_main(MsgType;locs;reply;f)(e)
⇐⇒ loc(e) ↓∈ locs
∧ ((header(e) = ``CLK msg`` ∈ Name) ∧ has-es-info-type(es;e;f;MsgType × ℤ))
∧ (d = 0 ∈ ℤ)
∧ (i = (snd((reply loc(e) (fst(msgval(e)))))) ∈ Id)
∧ (m = make-Msg(``CLK msg``;<fst((reply loc(e) (fst(msgval(e))))), CLK_ClockVal(MsgType;f)@e>) ∈ Message(f))}
Proof
Definitions occuring in Statement :
CLK_main: CLK_main(MsgType;locs;reply;f),
CLK_ClockFun: CLK_ClockVal(MsgType;f)@e,
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
msg-interface: Interface,
make-Msg: make-Msg(hdr;val),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
cons: [a / b],
nil: [],
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
guard: {T},
pi1: fst(t),
pi2: snd(t),
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
token: "$token",
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
int_seg_wf,
length_wf,
name_wf,
CLK_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
CLK_headers_fun_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
cons_member,
iff_weakening_equal,
classrel_wf,
msg-interface_wf,
CLK_main_wf,
make-msg-interface_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
CLK_headers_type_wf,
bag_wf,
Id_wf,
valueall-type_wf,
classrel-at,
CLK_Reply_wf,
iff_transitivity,
iff_weakening_uiff,
squash_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
eclass2-eclass1-classrel,
CLK_mk_reply_wf,
CLK_msg'base_wf,
CLK_Clock_wf,
base-classrel-equal,
subtype_rel_weakening,
ext-eq_weakening,
CLK_Clock-classrel,
has-es-info-type_wf,
es-info-body_wf,
equal-wf-base-T,
int_subtype_base,
CLK_ClockFun_wf,
equal-wf-T-base,
es-header_wf,
bag-member-spread-to-pi,
bag-member-single-weak,
subtype_rel_product,
top_wf,
subtype_top,
CLK_msg'send_wf,
single-bag_wf,
true_wf,
sq_stable__has-es-info-type,
member_wf,
equal-wf-base,
make-Msg_wf
Latex:
\mforall{}[MsgType:\{T:Type| valueall-type(T)\} ]. \mforall{}[locs:bag(Id)]. \mforall{}[reply:Id {}\mrightarrow{} MsgType {}\mrightarrow{} (MsgType \mtimes{} Id)].
\mforall{}[f:CLK\_headers\_type\{i:l\}(MsgType)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(f)].
\{<d, i, m> \mmember{} CLK\_main(MsgType;locs;reply;f)(e)
\mLeftarrow{}{}\mRightarrow{} loc(e) \mdownarrow{}\mmember{} locs
\mwedge{} ((header(e) = ``CLK msg``) \mwedge{} has-es-info-type(es;e;f;MsgType \mtimes{} \mBbbZ{}))
\mwedge{} (d = 0)
\mwedge{} (i = (snd((reply loc(e) (fst(msgval(e)))))))
\mwedge{} (m = make-Msg(``CLK msg``;<fst((reply loc(e) (fst(msgval(e))))), CLK\_ClockVal(MsgType;f)@e>)\000C)\}
Date html generated:
2015_07_23-PM-04_10_18
Last ObjectModification:
2015_02_04-PM-02_49_16
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