Nuprl Lemma : in-first-eclass
∀[Info,A:Type]. ∀Xs:EClass(A) List. ∀es:EO+(Info). ∀e:E. (↑e ∈b first-eclass(Xs) ⇐⇒ (∃X∈Xs. ↑e ∈b X))
Proof
Definitions occuring in Statement :
first-eclass: first-eclass(Xs),
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 :
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
non_neg_length,
length_wf_nat,
less_than_wf,
length_wf,
decidable__assert,
null_wf3,
subtype_rel_list,
top_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
list-cases,
l_exists_nil,
l_exists_wf_nil,
void_wf,
all_wf,
iff_wf,
assert_wf,
in-eclass_wf,
first-eclass_wf,
nil_wf,
product_subtype_list,
null_cons_lemma,
last-lemma-sq,
pos_length,
iff_transitivity,
not_wf,
equal-wf-T-base,
bnot_wf,
assert_of_null,
iff_weakening_uiff,
assert_of_bnot,
firstn_wf,
length_firstn,
decidable__le,
not-le-2,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
add-mul-special,
zero-mul,
add-zero,
le-add-cancel2,
subtract-is-less,
event-ordering+_cumulative2,
es-interface-subtype_rel2,
subtype_top,
l_exists_wf,
l_member_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
less-iff-le,
lelt_wf,
primrec-wf2,
sq_stable__le,
nat_wf,
list_wf,
list_accum_nil_lemma,
bag_size_empty_lemma,
last_wf,
l_exists_append,
cons_wf,
or_wf,
append_wf,
list_accum_append,
list_accum_cons_lemma,
list_accum_wf,
bag_wf,
empty-bag_wf,
eq_int_wf,
bag-size_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
eqtt_to_assert,
assert_of_eq_int,
assert_witness,
true_wf,
length_of_cons_lemma,
length_of_nil_lemma,
exists_wf,
select_wf,
length_nil,
length_wf_nil,
length_cons,
assert_functionality_wrt_uiff,
squash_wf,
set_subtype_base,
int_subtype_base,
minus-zero,
and_wf,
less_than_transitivity2,
le_weakening2
Latex:
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-eclass(Xs) \mLeftarrow{}{}\mRightarrow{} (\mexists{}X\mmember{}Xs. \muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_20-PM-03_17_54
Last ObjectModification:
2015_01_27-PM-10_50_22
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