Nuprl Lemma : global-order-pairwise-compat-msg-and-classrel
∀f:Name ─→ Type. ∀hdrs:Name List. ∀X:EClass(Interface).
(LocalClass(X)
⇒ (∀LL:(Id × Message(f)) List List
((∀L1,L2∈LL. L1 || L2)
⇒ (∀L∈LL.eo-msg-interface-constraint(global-eo(L);X;hdrs;f))
⇒ (∃G:(Id × Message(f)) List
(eo-msg-interface-constraint(global-eo(G);X;hdrs;f)
∧ (∀L∈LL.∃g:E ─→ E. ∀[e:E]. ∀[v:Interface]. (v ∈ X(e) ⇐⇒ v ∈ X(g e))))))))
Proof
Definitions occuring in Statement :
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
msg-interface: Interface,
Message: Message(f),
global-order-compat: L1 || L2,
global-eo: global-eo(L),
local-class: LocalClass(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
es-E: E,
Id: Id,
name: Name,
pairwise: (∀x,y∈L. P[x; y]),
l_all: (∀x∈L.P[x]),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
global-order-pairwise-compat-msg-interface-constraint,
embedding-preserves-local-class,
Message_wf,
msg-interface_wf,
global-eo_wf,
select_wf,
list_wf,
Id_wf,
sq_stable__le,
uall_wf,
es-E_wf,
event-ordering+_subtype,
iff_wf,
classrel_wf,
int_seg_wf,
length_wf,
eo-msg-interface-constraint_wf,
l_all_wf2,
l_member_wf,
exists_wf,
pairwise_wf,
global-order-compat_wf,
local-class_wf,
eclass_wf3,
name_wf
Latex:
\mforall{}f:Name {}\mrightarrow{} Type. \mforall{}hdrs:Name List. \mforall{}X:EClass(Interface).
(LocalClass(X)
{}\mRightarrow{} (\mforall{}LL:(Id \mtimes{} Message(f)) List List
((\mforall{}L1,L2\mmember{}LL. L1 || L2)
{}\mRightarrow{} (\mforall{}L\mmember{}LL.eo-msg-interface-constraint(global-eo(L);X;hdrs;f))
{}\mRightarrow{} (\mexists{}G:(Id \mtimes{} Message(f)) List
(eo-msg-interface-constraint(global-eo(G);X;hdrs;f)
\mwedge{} (\mforall{}L\mmember{}LL.\mexists{}g:E {}\mrightarrow{} E. \mforall{}[e:E]. \mforall{}[v:Interface]. (v \mmember{} X(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} X(g e))))))))
Date html generated:
2015_07_22-AM-11_59_38
Last ObjectModification:
2015_01_28-AM-08_41_49
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