Nuprl Lemma : list_of_extensions_in_fin_spr1
B:
List 
. b,a: List.
({(
(a 
fspr(B))) 
(||a|| = (||b|| + 1)) (firstn(||b||;a) = b)} 
(a list_of_extensions_in_fin_spr(B;b)))
Proof
Definitions occuring in Statement :
list_of_extensions_in_fin_spr: list_of_extensions_in_fin_spr(B;b),
list-in-fin_spr: (a fspr(B)),
firstn: firstn(n;as),
length: ||as||,
assert: b,
nat: ,
guard: {T},
all: x:A. B[x],
iff: P Q,
and: P Q,
function: x:A B[x],
add: n + m,
natural_number: $n,
equal: s = t,
l_member: (x l)
Definitions :
all: x:A. B[x],
guard: {T},
list_of_extensions_in_fin_spr: list_of_extensions_in_fin_spr(B;b),
member: t T,
implies: P Q,
exists: 
x:A. B[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
nat: ,
iff: P Q,
and: P Q,
rev_implies: P Q,
prop: 
,
int_seg: {i..j
},
lelt: i 
j < k,
so_lambda: 
x.t[x],
cand: A c B,
squash: 
T,
true: True,
length: ||as||,
le: A B,
l_member: (x l),
not: 
A,
false: False,
top: Top,
bfalse: ff,
assert: b,
bool: 
,
uall: [x:A]. B[x],
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
bnot: 
b,
or: P 
Q,
sq_type: SQType(T),
so_apply: x[s],
cons: Error :cons,
nil: Error :nil,
it: 
Lemmas :
list-in-fin_spr_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
Error :list_wf,
nat_wf,
assert_elim,
assert_wf,
length_wf_nat,
length_wf,
Error :zero-le-nat,
non_neg_length,
le_wf,
firstn_wf,
l_member_wf,
mklist_wf,
append_wf,
Error :cons_wf,
subtype_rel_sets,
lelt_wf,
Error :nil_wf,
int_seg_wf,
Error :firstn_last_sq,
Error :non_null_iff_length,
subtype_rel_list,
top_wf,
subtype_top,
set_subtype_base,
int_subtype_base,
list_subtype_base,
list-in-fin_spr_unfold_prp,
last_wf,
Error :isaxiom_wf_list,
Error :unit_subtype_list,
Error :axiom-list,
length_nil,
Error :product_subtype_list,
Error :non-axiom-list,
select_wf,
mklist_length,
mklist_select,
Error :mklist_member,
append_is_nil,
and_wf,
null_wf3,
btrue_wf,
btrue_neq_bfalse,
Error :length-append,
Error :firstn_append_front_singleton,
not_assert_elim,
Error :member-implies-null-eq-bfalse
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}b,a:\mBbbN{} List.
(\{(\muparrow{}(a \mmember{} fspr(B))) \mwedge{} (||a|| = (||b|| + 1)) \mwedge{} (firstn(||b||;a) = b)\}
\mLeftarrow{}{}\mRightarrow{} (a \mmember{} list\_of\_extensions\_in\_fin\_spr(B;b)))
Date html generated:
2013_03_20-AM-10_36_19
Last ObjectModification:
2013_03_19-PM-06_39_51
Home
Index