Nuprl Lemma : in_fspr_iff_in_spr_of_fin_spr
B:
List 
. f: . ((f 
spr(
a.if (a fspr(B)) then 0 else 1 fi )) 
(f fspr(B)))
Proof
Definitions occuring in Statement :
list-in-fin_spr: (a fspr(B)),
in_fin_spr: (f fspr(B)),
in_spr: (f spr(g)),
ifthenelse: if b then t else f fi ,
nat: ,
all: x:A. B[x],
iff: P Q,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n
Definitions :
all: x:A. B[x],
nat: ,
iff: P Q,
ifthenelse: if b then t else f fi ,
and: P 
Q,
implies: P Q,
rev_implies: P Q,
member: t T,
btrue: tt,
le: A 
B,
not: 
A,
false: False,
bfalse: ff,
exists: 
x:A. B[x],
in_fin_spr: (f fspr(B)),
squash: 
T,
true: True,
so_lambda: 
x.t[x],
int_seg: {i..j
},
lelt: i j < k,
in_spr: (f spr(g)),
mklist: mklist(n;f),
assert: 
b,
list-in-fin_spr: (a fspr(B)),
list_ind_reverse: Error :list_ind_reverse,
eq_int: (i =
j),
length: ||as||,
list_ind: Error :list_ind,
primrec: primrec(n;b;c),
nil: Error :nil,
it: 
,
ge: i 
j ,
nat_plus: 
,
top: Top,
cand: A c B,
prop: 
,
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),
guard: {T},
fin_spr: fin_spr(B),
so_apply: x[s],
sq_stable: SqStable(P)
Lemmas :
in_spr_wf,
list-in-fin_spr_wf,
bool_wf,
eqtt_to_assert,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
Error :list_wf,
nat_wf,
in_fin_spr_wf,
fin_spr_as_list,
all_wf,
mklist_wf,
subtype_rel_dep_function,
int_seg_wf,
subtype_rel_sets,
lelt_wf,
Error :sq_stable__le,
boolean_as_01,
nat_properties,
ge_wf,
Error :mklist_add1,
list-in-fin_spr_unfold_prp
\mforall{}B:\mBbbN{} List {}\mrightarrow{} \mBbbN{}. \mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbN{}. ((f \mmember{} spr(\mlambda{}a.if (a \mmember{} fspr(B)) then 0 else 1 fi )) \mLeftarrow{}{}\mRightarrow{} (f \mmember{} fspr(B)))
Date html generated:
2013_03_20-AM-10_35_58
Last ObjectModification:
2013_03_17-PM-03_49_42
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