Nuprl Lemma : list_of_lists_of_given_size_in_fin_spr1
B:
List 
. k:. a: List. ((
(a 
fspr(B))) 
(||a|| = k) 
(a list_of_lists_of_given_size_in_fin_spr(B;k)))
Proof
Definitions occuring in Statement :
list_of_lists_of_given_size_in_fin_spr: list_of_lists_of_given_size_in_fin_spr(B;k),
list-in-fin_spr: (a fspr(B)),
length: ||as||,
assert: b,
nat: ,
all: x:A. B[x],
iff: P Q,
and: P Q,
function: x:A B[x],
equal: s = t,
l_member: (x l)
Definitions :
all: x:A. B[x],
list_of_lists_of_given_size_in_fin_spr: list_of_lists_of_given_size_in_fin_spr(B;k),
member: t T,
primrec: primrec(n;b;c),
implies: P Q,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
nat: ,
iff: P Q,
and: P Q,
rev_implies: P Q,
prop: 
,
nil: Error :nil,
length: ||as||,
so_lambda: 
x.t[x],
list_ind: Error :list_ind,
it: 
,
assert: b,
ifthenelse: if b then t else f fi ,
eq_int: (i =
j),
btrue: tt,
true: True,
top: Top,
bfalse: ff,
exists: 
x:A. B[x],
squash: 
T,
cand: A c B,
int_iseg: {i...j},
guard: {T},
uall: [x:A]. B[x],
bool: 
,
unit: Unit,
uimplies: b supposing a,
sq_type: SQType(T),
so_apply: x[s],
uiff: uiff(P;Q),
bnot: 
b,
or: P 
Q,
nequal: a 
b T ,
cons: Error :cons
Lemmas :
nat_wf,
Error :list_wf,
nat_properties,
ge_wf,
member_singleton,
Error :isaxiom_wf_list,
bool_wf,
Error :unit_subtype_list,
Error :axiom-list,
Error :nil_wf,
Error :product_subtype_list,
Error :non-axiom-list,
non_neg_length,
length_wf_nat,
assert_wf,
list-in-fin_spr_wf,
le_wf,
l_member_wf,
Error :cons_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
list_subtype_base,
list-in-fin_spr_unfold,
equal_wf,
Error :primrec-unroll,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
Error :assert-bnot,
neg_assert_of_eq_int,
l-union-list_wf,
list-deq_wf,
nat-deq_wf,
map_wf,
list_of_extensions_in_fin_spr_wf,
top_wf,
list_of_lists_of_given_size_in_fin_spr_wf,
Error :non_null_iff_length,
subtype_rel_list,
subtype_top,
length_wf,
Error :firstn_last_sq,
length_firstn,
firstn_wf,
list-in-fin_spr_unfold_prp,
last_wf,
member-l-union-list,
member_map,
and_wf,
length_firstn_eq,
list_of_extensions_in_fin_spr1,
assert_functionality_wrt_uiff,
append_wf,
squash_wf,
true_wf,
firstn_last,
bnot_wf,
not_wf,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
Error :zero-le-nat
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}k:\mBbbN{}. \mforall{}a:\mBbbN{} List.
((\muparrow{}(a \mmember{} fspr(B))) \mwedge{} (||a|| = k) \mLeftarrow{}{}\mRightarrow{} (a \mmember{} list\_of\_lists\_of\_given\_size\_in\_fin\_spr(B;k)))
Date html generated:
2013_03_20-AM-10_36_43
Last ObjectModification:
2013_03_19-PM-07_18_01
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