Nuprl Lemma : first-eclass-val
∀[Info,A:Type].
∀Xs:EClass(A) List. ∀es:EO+(Info). ∀e:E.
(∃X∈Xs. (↑e ∈b X) ∧ (first-eclass(Xs)(e) = X(e) ∈ A)) supposing ↑e ∈b first-eclass(Xs)
Proof
Definitions occuring in Statement :
first-eclass: first-eclass(Xs),
eclass-val: X(e),
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_induction,
all_wf,
es-E_wf,
event-ordering+_subtype,
isect_wf,
assert_wf,
in-eclass_wf,
first-eclass_wf,
top_wf,
subtype_rel_list,
eclass_wf,
es-interface-subtype_rel2,
l_exists_wf,
l_member_wf,
eclass-val_wf,
assert_witness,
nil_wf,
cons_wf,
in-first-eclass,
l_exists_cons,
list_wf,
event-ordering+_wf,
bag_size_empty_lemma,
list_accum_nil_lemma,
decidable__assert,
sq_stable__le,
select_wf,
lelt_wf,
length_wf_nat,
non_neg_length,
length_wf,
false_wf,
length_of_cons_lemma,
bag_wf,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
add-swap,
minus-minus,
less-iff-le,
not-ge-2,
subtract_wf,
le_wf,
add-commutes,
minus-one-mul,
minus-add,
condition-implies-le,
not-le-2,
decidable__le,
nat_wf,
le-add-cancel,
zero-add,
add-zero,
add-associates,
add_functionality_wrt_le,
le_antisymmetry_iff,
spread_cons_lemma,
product_subtype_list,
list-cases,
colength_wf_list,
equal-wf-T-base,
bag-size_wf,
eq_int_wf,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties,
list_accum_cons_lemma,
member_wf,
assert_of_eq_int,
decidable__lt,
le_weakening,
single-valued-bag-if-le1,
bag-only_wf2,
neg_assert_of_eq_int,
assert-bnot,
bool_subtype_base,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
true_wf,
eqtt_to_assert,
bool_wf,
squash_wf,
not_wf,
length_wf_nil,
length_nil,
list_accum_wf,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
bool_cases,
ifthenelse_wf,
and_wf,
zero-le-nat,
bnot_wf,
not-equal-2
Latex:
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}X\mmember{}Xs. (\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (first-eclass(Xs)(e) = X(e))) supposing \muparrow{}e \mmember{}\msubb{} first-eclass(Xs)
Date html generated:
2015_07_20-PM-03_18_14
Last ObjectModification:
2015_07_16-AM-09_43_19
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