Nuprl Lemma : bag-member-sv-list
∀T:Type. ∀L:T List. ∀x:T. (x ↓∈ L ⇐⇒ (x ∈ L)) supposing single-valued-list(L;T)
Proof
Definitions occuring in Statement :
single-valued-list: single-valued-list(L;T),
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
bag-member: x ↓∈ bs
Lemmas :
l_member_wf,
bag-member_wf,
list-subtype-bag,
single-valued-list_wf,
list_wf,
false_wf,
le_wf,
member-permutation,
list-cases,
length_of_nil_lemma,
nil_member,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__lt,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
member_wf,
permutation_wf,
select_wf,
select_member,
lelt_wf,
length_wf,
less_than_wf,
sq_stable__le,
bag_wf
Latex:
\mforall{}T:Type. \mforall{}L:T List. \mforall{}x:T. (x \mdownarrow{}\mmember{} L \mLeftarrow{}{}\mRightarrow{} (x \mmember{} L)) supposing single-valued-list(L;T)
Date html generated:
2015_07_23-AM-11_26_19
Last ObjectModification:
2015_01_28-PM-11_15_52
Home
Index