Nuprl Lemma : is-first-class
∀[Info,A:Type]. ∀L:EClass(A) List. ∀es:EO+(Info). ∀e:E. (↑e ∈b first-class(L) ⇐⇒ (∃X∈L. ↑e ∈b X))
Proof
Definitions occuring in Statement :
first-class: first-class(L),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
l_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Lemmas :
list_induction,
all_wf,
es-E_wf,
event-ordering+_subtype,
iff_wf,
assert_wf,
in-eclass_wf,
first-class_wf,
top_wf,
subtype_rel_list,
eclass_wf,
es-interface-subtype_rel2,
l_exists_wf,
l_member_wf,
reduce_nil_lemma,
isempty_lemma,
reduce_cons_lemma,
list_wf,
event-ordering+_wf,
false_wf,
stuck-spread,
base_wf,
length_of_nil_lemma,
less_than_transitivity1,
less_than_irreflexivity,
l_exists_wf_nil,
cons_wf,
cond-class_wf,
l_exists_cons,
is-cond-class,
or_wf,
sq_stable__le,
select_wf,
length_wf,
int_seg_wf,
exists_wf
\mforall{}[Info,A:Type]. \mforall{}L:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-class(L) \mLeftarrow{}{}\mRightarrow{} (\mexists{}X\mmember{}L. \muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_17-PM-00_50_38
Last ObjectModification:
2015_02_02-PM-06_40_47
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