Nuprl Lemma : local-class-predicate-property2
∀[Info,A:Type]. ∀[X1,X2:EClass(A)]. ∀[F:Id ⟶ hdataflow(Info;A)].
(local-class-predicate{i:l}(F;Info;A;X1)) supposing
(local-class-predicate{i:l}(F;Info;A;X2) and
(∀es:EO+(Info). ∀e:E. (X1(e) = X2(e) ∈ bag(A))))
Proof
Definitions occuring in Statement :
local-class-predicate: local-class-predicate{i:l}(F;Info;A;X),
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
hdataflow: hdataflow(A;B),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-class-predicate: local-class-predicate{i:l}(F;Info;A;X),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X1,X2:EClass(A)]. \mforall{}[F:Id {}\mrightarrow{} hdataflow(Info;A)].
(local-class-predicate\{i:l\}(F;Info;A;X1)) supposing
(local-class-predicate\{i:l\}(F;Info;A;X2) and
(\mforall{}es:EO+(Info). \mforall{}e:E. (X1(e) = X2(e))))
Date html generated:
2016_05_16-PM-02_04_53
Last ObjectModification:
2015_12_29-PM-02_24_59
Theory : event-ordering
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