Nuprl Lemma : verify-classrel
∀[T:Type]. ∀[f:Name ⟶ Type]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[v:T]. ∀[hdr:Name].
uiff(v ∈ Verify(hdr)(e);(↑es-info-auth(es;e)) ∧ (header(e) = hdr ∈ Name) ∧ v = body(e)) supposing hdr encodes T
Proof
Definitions occuring in Statement :
verify-class: Verify(hdr),
encodes-msg-type: hdr encodes T,
es-info-auth: es-info-auth(es;e),
equal-info-body: v = body(e),
es-header: header(e),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
name: Name,
assert: ↑b,
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,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
equal-info-body: v = body(e),
has-es-info-type: has-es-info-type(es;e;f;T),
subtype_rel: A ⊆r B,
prop: ℙ,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
verify-class: Verify(hdr),
cond-verify-msg-body: cond-verify-msg-body(hdr;msg),
cond-msg-body: cond-msg-body(hdr;msg),
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
false: False,
encodes-msg-type: hdr encodes T,
msg-type: msg-type(msg;f),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-header: header(e),
es-info-body: msgval(e),
cand: A c∧ B,
es-info-auth: es-info-auth(es;e),
top: Top,
not: ¬A,
bool: 𝔹,
unit: Unit,
it: ⋅,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
rev_uimplies: rev_uimplies(P;Q)
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{} Verify(hdr)(e);(\muparrow{}es-info-auth(es;e)) \mwedge{} (header(e) = hdr) \mwedge{} v = body(e))
supposing hdr encodes T
Date html generated:
2016_05_17-AM-09_13_06
Last ObjectModification:
2016_01_17-PM-11_15_06
Theory : classrel!lemmas
Home
Index