{ 
[T:Type]. ((x,y:T. Dec(x = y)) 
(L:T List. |{x:T| (x 
L)} | 
||L||)) }
{ Proof }
Definitions occuring in Statement :
length: ||as||,
decidable: Dec(P),
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
list: type List,
universe: Type,
equal: s = t,
l_member: (x l),
cardinality-le: |T| n
Definitions :
tactic: Error :tactic,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
l_member: (x l),
set: {x:A| B[x]} ,
function: x:A 
B[x],
int_seg: {i..j
},
surject: Surj(A;B;f),
product: x:A 
B[x],
exists: 
x:A. B[x],
cardinality-le: |T| n,
universe: Type,
all: x:A. B[x],
list: type List,
prop: 
,
equal: s = t,
decidable: Dec(P),
implies: P Q,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A B,
or: P 
Q,
union: left + right,
strong-subtype: strong-subtype(A;B),
member: t T,
limited-type: LimitedType,
bool: 
,
nil: [],
nat: 
,
cand: A c B,
sq_stable: SqStable(P),
squash: 
T,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
assert: 
b,
valueall-type: valueall-type(T),
value-type: value-type(T),
no_repeats: no_repeats(T;l),
prime_ideal_p: IsPrimeIdeal(R;P),
integ_dom_p: IsIntegDom(r),
grp_leq: a b,
monoid_hom_p: IsMonHom{M1,M2}(f),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
action_p: IsAction(A;x;e;S;f),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
bilinear: BiLinear(T;pl;tm),
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
coprime: CoPrime(a,b),
uconnex: uconnex(T; x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inject: Inj(A;B;f),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
iff: P 
Q,
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
i-closed: i-closed(I),
i-finite: i-finite(I),
sq_exists: x:{A| B[x]},
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
infix_ap: x f y,
apply: f a,
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
l_disjoint: l_disjoint(T;l1;l2),
prime: prime(a),
reducible: reducible(a),
l_contains: A B,
IdLnk: IdLnk,
Id: Id,
fset: FSet{T},
dstype: dstype(TypeNames; d; a),
atom: Atom$n,
rationals: 
,
nat_plus: 
,
so_lambda: 
x.t[x],
true: True,
select: l[i],
remove-repeats: remove-repeats(eq;L),
last: last(L),
hd: hd(l),
cons: [car / cdr]
Lemmas :
l_member-set,
decidable__equal_set,
decidable__l_member,
sq_stable_from_decidable,
cardinality-le_wf,
surject_wf,
int_seg_wf,
decidable_wf,
list-cardinality-le,
member_wf,
subtype_rel_wf,
list-subtype,
nat_wf,
l_member_wf
\mforall{}[T:Type]. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}L:T List. |\{x:T| (x \mmember{} L)\} | \mleq{} ||L||))
Date html generated:
2011_08_10-AM-07_48_44
Last ObjectModification:
2011_06_18-AM-08_13_09
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