Nuprl Lemma : fin_spr_is_spr
B:
List 
. spr(
a.if (a 
fspr(B)) then 0 else 1 fi )
Proof
Definitions occuring in Statement :
list-in-fin_spr: (a fspr(B)),
ifthenelse: if b then t else f fi ,
nat: ,
all: x:A. B[x],
lambda: x.A[x],
function: x:A B[x],
natural_number: $n
Definitions :
all: x:A. B[x],
nat: ,
spr: spr(g),
ifthenelse: if b then t else f fi ,
and: P 
Q,
implies: P 
Q,
exists: 
x:A. B[x],
gt: i > j,
member: t T,
btrue: tt,
le: A 
B,
not: 
A,
false: False,
bfalse: ff,
squash: 
T,
true: True,
so_lambda: 
x.t[x],
assert: 
b,
top: Top,
band: p 
q,
prop: 
,
cand: A c B,
iff: P 
Q,
rev_implies: P Q,
uall: [x:A]. B[x],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
bnot: b,
or: P 
Q,
sq_type: SQType(T),
guard: {T},
so_apply: x[s],
it: 
Lemmas :
equal_wf,
nat_wf,
list-in-fin_spr_wf,
bool_wf,
eqtt_to_assert,
le_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
gt_wf,
Error :list_wf,
bool_cases,
assert_of_bnot,
subtype_rel_set_simple,
append_wf,
Error :cons_wf,
Error :nil_wf,
list-in-fin_spr_unfold,
assert_elim,
and_wf,
ifthenelse_wf,
eq_int_wf,
length_wf,
subtype_rel_list,
assert_of_eq_int,
neg_assert_of_eq_int,
top_wf,
subtype_top,
Error :last_append_singleton_sq,
int_subtype_base,
Error :zero-le-nat,
iff_transitivity,
assert_wf,
le_int_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_le_int,
Error :firstn_append_front_singleton,
not_assert_elim,
length_nil,
non_neg_length,
length_wf_nil,
length_wf_nat,
length_cons,
length_append,
not_wf
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. spr(\mlambda{}a.if (a \mmember{} fspr(B)) then 0 else 1 fi )
Date html generated:
2013_03_20-AM-10_35_49
Last ObjectModification:
2013_03_11-PM-04_51_50
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