Nuprl Lemma : member-eclass-eclass2-eclass3-eclass1
∀[Info,A,B,C,D:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[Z:EClass(C)]. ∀[f:Id ─→ A ─→ B ─→ C ─→ bag(D)]. ∀[es:EO+(Info)].
∀[e:E].
(uiff(↑e ∈b (eclass3((f o X);Y) o Z);(↑e ∈b X)
∧ (↑e ∈b Y)
∧ (↑e ∈b Z)
∧ (¬↑bag-null(f loc(e) X@e Y@e Z@e)))) supposing
(single-valued-classrel(es;X;A) and
single-valued-classrel(es;Y;B) and
single-valued-classrel(es;Z;C))
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
eclass2: (X o Y),
eclass1: (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_witness,
assert_wf,
member-eclass_wf,
eclass2_wf,
eclass3_wf,
bag_wf,
eclass1_wf,
not_wf,
bag-null_wf,
es-loc_wf,
classfun-res_wf,
event-ordering+_subtype,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
eclass_wf,
assert-member-eclass,
sq_stable__and,
sq_stable__assert,
sq_stable__not,
squash_wf,
eclass2-classrel,
classrel-implies-member,
eclass3-classrel,
eclass1-classrel,
classrel-classfun-res,
assert-bag-null,
bag-member-empty,
bag-member_wf,
true_wf,
iff_weakening_equal,
bag-member-not-bag-null,
classrel_wf,
exists_wf
Latex:
\mforall{}[Info,A,B,C,D:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)]. \mforall{}[f:Id
{}\mrightarrow{} A
{}\mrightarrow{} B
{}\mrightarrow{} C
{}\mrightarrow{} bag(D)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(uiff(\muparrow{}e \mmember{}\msubb{} (eclass3((f o X);Y) o Z);(\muparrow{}e \mmember{}\msubb{} X)
\mwedge{} (\muparrow{}e \mmember{}\msubb{} Y)
\mwedge{} (\muparrow{}e \mmember{}\msubb{} Z)
\mwedge{} (\mneg{}\muparrow{}bag-null(f loc(e) X@e Y@e Z@e)))) supposing
(single-valued-classrel(es;X;A) and
single-valued-classrel(es;Y;B) and
single-valued-classrel(es;Z;C))
Date html generated:
2015_07_23-AM-11_28_40
Last ObjectModification:
2015_02_04-PM-04_46_06
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