Nuprl Lemma : fin_spr_as_list
f:
. B: List . ((x:. (if (mklist(x;f) 
fspr(B)) then 0 else 1 fi = 0)) 
(f fin_spr(B)))
Proof
Definitions occuring in Statement :
list-in-fin_spr: (a fspr(B)),
fin_spr: fin_spr(B),
ifthenelse: if b then t else f fi ,
nat: ,
all: x:A. B[x],
implies: P Q,
member: t T,
function: x:A B[x],
natural_number: $n,
equal: s = t,
mklist: mklist(n;f)
Definitions :
all: x:A. B[x],
nat: ,
implies: P Q,
ifthenelse: if b then t else f fi ,
member: t T,
so_lambda: 
x.t[x],
int_seg: {i..j
},
le: A 
B,
btrue: tt,
not: 
A,
false: False,
bfalse: ff,
exists: 
x:A. B[x],
fin_spr: fin_spr(B),
squash: 
T,
true: True,
top: Top,
and: P 
Q,
iff: P 
Q,
rev_implies: P Q,
prop: 
,
nat_plus: 
,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
uimplies: b supposing a,
lelt: i j < k,
unit: Unit,
assert: 
b,
uiff: uiff(P;Q),
bnot: 
b,
or: P 
Q,
sq_type: SQType(T),
guard: {T},
band: p q,
it: 
Lemmas :
all_wf,
nat_wf,
equal_wf,
list-in-fin_spr_wf,
mklist_wf,
subtype_rel_dep_function,
int_seg_wf,
subtype_rel_set_simple,
le_wf,
subtype_rel_sets,
lelt_wf,
subtype_rel_weakening,
ext-eq_weakening,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
Error :list_wf,
bool_cases,
assert_of_bnot,
list-in-fin_spr_unfold,
int_subtype_base,
mklist_length,
eq_int_wf,
assert_wf,
bnot_wf,
not_wf,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
firstn_wf,
assert_of_le_int,
last_wf,
Error :non_null_iff_length,
subtype_rel_list,
top_wf,
subtype_top,
squash_wf,
true_wf,
Error :last_mklist,
subtype_rel_self,
Error :firstn-mklist1
\mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbN{}. \mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}.
((\mforall{}x:\mBbbN{}. (if (mklist(x;f) \mmember{} fspr(B)) then 0 else 1 fi = 0)) {}\mRightarrow{} (f \mmember{} fin\_spr(B)))
Date html generated:
2013_03_20-AM-10_35_33
Last ObjectModification:
2013_03_11-PM-04_24_05
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