{ 
t:
. A:Id List.
( {a:Id| (a 
A)} ~ (2 * t) + 1
(W:{a:Id| (a A)} List List
((ws:{a:Id| (a A)} List
((ws W) 
(||ws|| = (t + 1)) 
no_repeats({a:Id| (a A)} ;ws)\000C
))
two-intersection(A;W)))) }
{ Proof }
Definitions occuring in Statement :
two-intersection: two-intersection(A;W),
Id: Id,
length: ||as||,
int_seg: {i..j
},
nat: ,
all: x:A. B[x],
iff: P Q,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
list: type List,
multiply: n * m,
add: n + m,
natural_number: $n,
int: 
,
equal: s = t,
no_repeats: no_repeats(T;l),
l_member: (x l),
equipollent: A ~ B
Definitions :
list: type List,
equipollent: A ~ B,
function: x:A 
B[x],
all: x:A. B[x],
member: t T,
nat: ,
equal: s = t,
le: A 
B,
universe: Type,
prop: 
,
int: ,
less_than: a < b,
void: Void,
implies: P Q,
false: False,
not: 
A,
p-outcome: Outcome,
subtype_rel: A 
r B,
strong-subtype: strong-subtype(A;B),
product: x:A 
B[x],
exists: 
x:A. B[x],
rev_implies: P Q,
no_repeats: no_repeats(T;l),
iff: P Q,
guard: {T},
rationals: 
,
subtype: S T,
real: 
,
add: n + m,
n-intersecting: n-intersecting(A;T;n),
grp_car: Error :grp_car,
multiply: n * m,
int_seg: {i..j},
length: ||as||,
and: P Q,
two-intersection: two-intersection(A;W),
Id: Id,
l_member: (x l),
set: {x:A| B[x]} ,
natural_number: $n,
l_all: (xL.P[x]),
so_lambda: 
x.t[x],
subtract: n - m,
combination: Combination(n;T),
Auto: Error :Auto,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
tactic: Error :tactic,
fpf: a:A fp-> B[a],
CollapseTHENA: Error :CollapseTHENA,
biject: Bij(A;B;f),
bool: 
,
cand: A c B,
isect: 
x:A. B[x],
top: Top,
ge: i 
j ,
label: ...$L... t,
pair: <a, b>,
tl: tl(l),
hd: hd(l),
MaAuto: Error :MaAuto,
nil: [],
cons: [car / cdr],
THENM: Error :THENM,
lambda: x.A[x],
RepeatFor: Error :RepeatFor,
ParallelOp: Error :ParallelOp
Lemmas :
l_all_cons,
nat_properties,
length_nil,
length_cons,
non_neg_length,
length_wf_nat,
top_wf,
combination_wf,
subtype_rel_wf,
l_all_wf,
two-intersection_wf,
iff_wf,
length_wf1,
no_repeats_wf,
equipollent_wf,
l_member_wf,
int_seg_wf,
Id_wf,
combinations-n-intersecting,
nat_wf,
member_wf,
le_wf
\mforall{}t:\mBbbN{}. \mforall{}A:Id List.
( \{a:Id| (a \mmember{} A)\} \msim{} \mBbbN{}(2 * t) + 1
{}\mRightarrow{} (\mforall{}W:\{a:Id| (a \mmember{} A)\} List List
((\mforall{}ws:\{a:Id| (a \mmember{} A)\} List. ((ws \mmember{} W) \mLeftarrow{}{}\mRightarrow{} (||ws|| = (t + 1)) \mwedge{} no\_repeats(\{a:Id| (a \mmember{} A)\} ;\000C
ws)))
{}\mRightarrow{} two-intersection(A;W))))
Date html generated:
2010_08_27-AM-12_50_26
Last ObjectModification:
2009_12_23-PM-03_26_44
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