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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
has-es-info-type: has-es-info-type(es;e;f;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
encodes-msg-type: hdr encodes T,
uiff: uiff(P;Q),
squash: ↓T,
equal-info-body: v = body(e),
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
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:
2016_05_17-AM-09_12_58
Last ObjectModification:
2016_01_17-PM-11_15_24
Theory : classrel!lemmas
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