Nuprl Lemma : longer-list-not-member
[T:Type]
eq:x,y:T. Dec(x = y). L1,L2:T List.
(no_repeats(T;L1) 
no_repeats(T;L2) (||L2|| > ||L1||) (
x:T. ((x 
L2) 
(
(x L1)))))
Proof not projected
Definitions occuring in Statement :
length: ||as||,
decidable: Dec(P),
uall: [x:A]. B[x],
gt: i > j,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
list: type List,
universe: Type,
equal: s = t,
no_repeats: no_repeats(T;l),
l_member: (x l)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
gt: i > j,
length: ||as||,
ycomb: Y,
false: False,
member: t T,
prop: 
,
or: P 
Q,
exists: x:A. B[x],
and: P Q,
cand: A c B,
decision: Decision,
top: Top,
subtype: S 
T,
not: A,
append: as @ bs,
rev_implies: P 
Q,
iff: P Q,
squash: 
T,
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
ge: i 
j ,
le: A 
B,
decidable: Dec(P),
uimplies: b supposing a,
uiff: uiff(P;Q),
isl: isl(x),
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
guard: {T},
bool: 
,
unit: Unit,
it: 
,
dec2bool: dec2bool(d)
Lemmas :
non_neg_length,
gt_wf,
length_wf1,
no_repeats_wf,
decidable_wf,
l_member_decidable,
remove-first_wf,
isl_wf,
not_wf,
l_member_wf,
no_repeats_cons,
cons_member,
no_repeats-remove-first,
length-remove-first,
assert_wf,
dec2bool_wf,
top_wf,
not_functionality_wrt_iff,
dec2bool_decidable,
member_append,
nil_member,
squash_wf,
true_wf,
remove-first-cons,
member_singleton,
bool_wf,
bnot_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[T:Type]
\mforall{}eq:\mforall{}x,y:T. Dec(x = y). \mforall{}L1,L2:T List.
(no\_repeats(T;L1) {}\mRightarrow{} no\_repeats(T;L2) {}\mRightarrow{} (||L2|| > ||L1||) {}\mRightarrow{} (\mexists{}x:T. ((x \mmember{} L2) \mwedge{} (\mneg{}(x \mmember{} L1)))))
Date html generated:
2011_10_20-PM-03_44_16
Last ObjectModification:
2011_08_29-PM-06_49_05
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