Nuprl Lemma : member-eclass-simple-loc-comb-1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[F:Id ─→ bag(A) ─→ bag(B)]. ∀[X:EClass(A)].
(↑e ∈b F(Loc, X)) supposing ((∀loc:Id. ∀as:bag(A). ((¬↑bag-null(as)) ⇒ (¬↑bag-null(F loc as)))) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
simple-loc-comb-1: F(Loc, X),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Lemmas :
member-eclass_wf,
simple-loc-comb-1_wf,
all_wf,
Id_wf,
bag_wf,
not_wf,
assert_wf,
bag-null_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-loc_wf,
assert-bag-null-sq,
subtype_rel_bag,
top_wf,
member-eclass-iff-size,
bag_size_empty_lemma,
null-bag-size,
assert-bag-null,
equal-wf-T-base,
iff_transitivity,
bnot_wf,
iff_weakening_uiff,
assert_of_bnot
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[F:Id {}\mrightarrow{} bag(A) {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)].
(\muparrow{}e \mmember{}\msubb{} F(Loc, X)) supposing
((\mforall{}loc:Id. \mforall{}as:bag(A). ((\mneg{}\muparrow{}bag-null(as)) {}\mRightarrow{} (\mneg{}\muparrow{}bag-null(F loc as)))) and
(\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_23-AM-11_27_45
Last ObjectModification:
2015_01_28-PM-11_13_45
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