Nuprl Lemma : single-valued-base-classrel
∀[f:Name ⟶ Type]. ∀[T:Type]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[v1,v2:T]. ∀[hdr:Name].
v1 ∈ Base(hdr)(e) ⇒ v2 ∈ Base(hdr)(e) ⇒ (v1 = v2 ∈ T) supposing T = (f hdr) ∈ Type
Proof
Definitions occuring in Statement :
base-headers-msg-val: Base(hdr),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
name: Name,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: 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],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
encodes-msg-type: hdr encodes T,
uiff: uiff(P;Q),
and: P ∧ Q,
name: Name,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[T:Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[v1,v2:T]. \mforall{}[hdr:Name].
v1 \mmember{} Base(hdr)(e) {}\mRightarrow{} v2 \mmember{} Base(hdr)(e) {}\mRightarrow{} (v1 = v2) supposing T = (f hdr)
Date html generated:
2016_05_17-AM-09_28_34
Last ObjectModification:
2015_12_29-PM-04_02_04
Theory : classrel!lemmas
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