Nuprl Lemma : member-eclass-simple-comb-1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[F:bag(A) ─→ bag(B)]. ∀[X:EClass(A)].
(↑e ∈b F|X|) supposing ((∀as:bag(A). ((¬↑bag-null(as)) ⇒ (¬↑bag-null(F as)))) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
simple-comb-1: F|X|,
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
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 :
assert-bag-null-sq,
subtype_rel_bag,
top_wf,
member-eclass-iff-size,
bag_size_empty_lemma,
assert_wf,
bag-null_wf,
null-bag-size,
assert-bag-null,
equal-wf-T-base,
bag_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
member-eclass_wf,
simple-comb-1_wf,
all_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[F:bag(A) {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)].
(\muparrow{}e \mmember{}\msubb{} F|X|) supposing ((\mforall{}as:bag(A). ((\mneg{}\muparrow{}bag-null(as)) {}\mRightarrow{} (\mneg{}\muparrow{}bag-null(F as)))) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_23-AM-11_27_06
Last ObjectModification:
2015_01_28-PM-11_14_03
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