Nuprl Lemma : length-eq-lists-diff-elts
[T:Type]
eq:x,y:T. Dec(x = y). L1,L2:T List.
(no_repeats(T;L1)
no_repeats(T;L2)
(||L1|| 
||L2|| )
(
x:T. ((x 
L2) 
(
(x L1))))
(x:T. ((x L1) ((x L2)))))
Proof not projected
Definitions occuring in Statement :
length: ||as||,
decidable: Dec(P),
uall: [x:A]. B[x],
ge: 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,
length: ||as||,
exists: x:A. B[x],
and: P Q,
ycomb: Y,
member: t T,
prop: 
,
append: as @ bs,
iff: P 
Q,
rev_implies: P Q,
top: Top,
subtype: S 
T,
ge: i j ,
not: A,
or: P 
Q,
le: A 
B,
false: False,
so_lambda: 
x.t[x],
label: ...$L... t,
decision: Decision,
uimplies: b supposing a,
uiff: uiff(P;Q),
decidable: Dec(P),
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
sq_type: SQType(T),
guard: {T},
isl: isl(x),
dec2bool: dec2bool(d)
Lemmas :
nil_member,
l_member_wf,
not_wf,
ge_wf,
length_wf1,
no_repeats_wf,
member_append,
no_repeats_cons,
decidable_wf,
or_functionality_wrt_iff,
member_singleton,
non_neg_length,
length_wf_nat,
top_wf,
l_member_decidable,
cons_member,
not_functionality_wrt_iff,
not_over_or,
exists_functionality_wrt_iff,
and_functionality_wrt_iff,
append_wf,
remove-first_wf,
isl_wf,
no_repeats-remove-first,
remove-first-member-implies,
length-remove-first,
subtype_base_sq,
int_subtype_base,
remove-first-no_repeats-member,
dec2bool_decidable,
assert_wf,
assert_of_bnot,
dec2bool_wf
\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{} (||L1|| \mgeq{} ||L2|| )
{}\mRightarrow{} (\mexists{}x:T. ((x \mmember{} L2) \mwedge{} (\mneg{}(x \mmember{} L1))))
{}\mRightarrow{} (\mexists{}x:T. ((x \mmember{} L1) \mwedge{} (\mneg{}(x \mmember{} L2)))))
Date html generated:
2011_10_20-PM-03_44_28
Last ObjectModification:
2011_08_30-PM-08_00_24
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