{ 
[A:Type]
d:A List. x:A. eq:EqDecider(A).
((x 
d) 
(
i:
||d||. ((j:i. (
(d[j] = x))) 
(d[i] = x)))) }
{ Proof }
Definitions occuring in Statement :
select: l[i],
length: ||as||,
int_seg: {i..j
},
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_member: (x l),
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
length: ||as||,
member: t T,
prop: 
,
ycomb: Y,
exists: x:A. B[x],
and: P Q,
not: A,
select: l[i],
top: Top,
subtype: S 
T,
ifthenelse: if b then t else f fi ,
le_int: i 
z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
false: False,
int_seg: {i..j},
cand: A c B,
lelt: i j < k,
le: A B,
rev_implies: P 
Q,
iff: P Q,
squash: 
T,
true: True,
bool: 
,
unit: Unit,
uimplies: b supposing a,
or: P 
Q,
decidable: Dec(P),
sq_type: SQType(T),
guard: {T},
it: 
Lemmas :
nil_member,
l_member_wf,
deq_wf,
eqof_wf,
bool_wf,
iff_weakening_uiff,
assert_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
uiff_inversion,
deq_property,
not_functionality_wrt_uiff,
non_neg_length,
length_wf_nat,
top_wf,
select_wf,
length_wf1,
int_seg_wf,
length_cons,
cons_member,
int_seg_properties,
le_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
squash_wf,
true_wf,
select_cons_tl,
select_cons_tl_sq
\mforall{}[A:Type]
\mforall{}d:A List. \mforall{}x:A. \mforall{}eq:EqDecider(A).
((x \mmember{} d) {}\mRightarrow{} (\mexists{}i:\mBbbN{}||d||. ((\mforall{}j:\mBbbN{}i. (\mneg{}(d[j] = x))) \mwedge{} (d[i] = x))))
Date html generated:
2011_08_10-AM-07_55_45
Last ObjectModification:
2011_06_18-AM-08_16_51
Home
Index