Nuprl Lemma : base-noloc-classrel
∀[T:Type]. ∀[f:Name ⟶ Type]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[v:T]. ∀[hdr:Name].
uiff(v ∈ Base(hdr)(e);(header(e) = hdr ∈ Name) ∧ has-es-info-type(es;e;f;T) ∧ (v = msgval(e) ∈ T))
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),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
name: Name,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
has-es-info-type: has-es-info-type(es;e;f;T),
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
base-headers-msg-val: Base(hdr),
cond-msg-body: cond-msg-body(hdr;msg),
encodes-msg-type: hdr encodes T,
guard: {T},
msg-type: msg-type(msg;f),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-header: header(e),
es-info-body: msgval(e),
top: Top,
false: False,
or: P ∨ Q,
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[T:Type]. \mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[v:T]. \mforall{}[hdr:Name].
uiff(v \mmember{} Base(hdr)(e);(header(e) = hdr) \mwedge{} has-es-info-type(es;e;f;T) \mwedge{} (v = msgval(e)))
supposing hdr encodes T
Date html generated:
2016_05_17-AM-09_12_47
Last ObjectModification:
2016_01_17-PM-11_15_39
Theory : classrel!lemmas
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