Nuprl Lemma : eclass1-base-classrel
∀[T,C:Type]. ∀[f:Name ─→ Type]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[v:C]. ∀[hdr:Name]. ∀[g:Id ─→ T ─→ C].
uiff(v ∈ (g o Base(hdr))(e);(header(e) = hdr ∈ Name) ∧ has-es-info-type(es;e;f;T) ∧ (v = (g loc(e) msgval(e)) ∈ C))
supposing hdr encodes T
Proof
Definitions occuring in Statement :
base-headers-msg-val: Base(hdr),
encodes-msg-type: hdr encodes T,
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
eclass1: (f o X),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
encodes-msg-type_wf,
Id_wf,
name_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
classrel_wf,
eclass1_wf,
base-headers-msg-val_wf,
es-header_wf,
has-es-info-type_wf,
es-info-body_wf,
es-loc_wf,
equal_wf,
squash_wf,
equal-info-body_wf,
uiff_wf,
sq_stable__has-es-info-type,
exists_wf,
base-classrel-equal,
iff_weakening_uiff,
eclass1-classrel,
sq_stable__uiff,
sq_stable__classrel,
sq_stable__and,
sq_stable__equal
Latex:
\mforall{}[T,C:Type]. \mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[v:C]. \mforall{}[hdr:Name].
\mforall{}[g:Id {}\mrightarrow{} T {}\mrightarrow{} C].
uiff(v \mmember{} (g o Base(hdr))(e);(header(e) = hdr)
\mwedge{} has-es-info-type(es;e;f;T)
\mwedge{} (v = (g loc(e) msgval(e))))
supposing hdr encodes T
Date html generated:
2015_07_22-PM-00_06_17
Last ObjectModification:
2015_01_28-AM-11_43_15
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