Nuprl Lemma : member-eclass-eclass0
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ─→ B ─→ bag(C)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(↑e ∈b (f o X);(↑e ∈b X) ∧ (¬↑bag-null(f loc(e) X@e))) supposing single-valued-classrel(es;X;B)
Proof
Definitions occuring in Statement :
eclass0: (f o X),
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Lemmas :
assert-member-eclass,
eclass0-classrel,
classrel_wf,
assert_wf,
bag-null_wf,
es-loc_wf,
classfun-res_wf,
event-ordering+_subtype,
assert_witness,
member-eclass_wf,
eclass0_wf,
not_wf,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
classrel-classfun-res,
classrel-implies-member,
bag-member_wf,
assert-bag-null,
bag-member-empty-iff,
bag-member-not-bag-null
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (f o X);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\mneg{}\muparrow{}bag-null(f loc(e) X@e)))
supposing single-valued-classrel(es;X;B)
Date html generated:
2015_07_23-AM-11_28_18
Last ObjectModification:
2015_01_28-PM-11_13_41
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