{ 
[L:{dv:ClassDerivation| WF(dv)} List]. [n:
]. [m:{m:| 0 < (n + m)} ].
(cdv-argtype(pack-cdv-args(n;m;L))
= (k:||L|| 
bag(map(
dv.hd(cdv-types(dv));L)[k]))) supposing
((||L|| = (n + m)) and
(dv
L.||cdv-types(dv)|| = 1)) }
{ Proof }
Definitions occuring in Statement :
pack-cdv-args: pack-cdv-args(n;m;L),
cdv-wf: WF(dv),
cdv-argtype: cdv-argtype(dv),
cdv-types: cdv-types(dv),
classderiv: ClassDerivation,
select: l[i],
hd: hd(l),
map: map(f;as),
length: ||as||,
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
less_than: a < b,
set: {x:A| B[x]} ,
lambda: x.A[x],
function: x:A B[x],
list: type List,
add: n + m,
natural_number: $n,
int: 
,
universe: Type,
equal: s = t,
l_all: (xL.P[x]),
bag: bag(T)
Definitions :
l_member: (x l),
real: 
,
grp_car: |g|,
subtype: S 
T,
limited-type: LimitedType,
eclass: EClass(A[eo; e]),
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
implies: P 
Q,
false: False,
not: 
A,
le: A 
B,
add: n + m,
axiom: Ax,
pack-cdv-args: pack-cdv-args(n;m;L),
cdv-argtype: cdv-argtype(dv),
list: type List,
uall: [x:A]. B[x],
less_than: a < b,
nat: ,
so_lambda: 
x.t[x],
set: {x:A| B[x]} ,
cdv-wf: WF(dv),
classderiv: ClassDerivation,
l_all: (xL.P[x]),
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t T,
int: ,
prop: 
,
cdv-types: cdv-types(dv),
hd: hd(l),
lambda: x.A[x],
map: map(f;as),
select: l[i],
bag: bag(T),
length: ||as||,
natural_number: $n,
int_seg: {i..j},
function: x:A B[x],
list-to-cdv: list-to-cdv(L),
universe: Type,
equal: s = t,
sqequal: s ~ t,
rev_uimplies: rev_uimplies(P;Q),
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bnot: b,
bimplies: p q,
band: p q,
bor: p 
q,
true: True,
lt_int: i <z j,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
listp: A List
,
assert: 
b,
tl: tl(l),
classderiv_ind: classderiv_ind,
sq_type: SQType(T),
append: as @ bs,
iff: P 
Q,
combination: Combination(n;T),
void: Void,
top: Top,
concat: concat(ll),
cons: [car / cdr],
nil: [],
lelt: i j < k,
rationals: 
,
cdvpair-fst: cdvpair-fst(x),
classderiv_ind_cdvpair: classderiv_ind_cdvpair_compseq_tag_def,
cdvpair-snd: cdvpair-snd(x),
cdvbase?: cdvbase?(x),
cdvpair?: cdvpair?(x),
cdvdelay?: cdvdelay?(x),
cdvcomb?: cdvcomb?(x),
cdvreccomb?: cdvreccomb?(x),
cdvdelay-X: cdvdelay-X(x),
classderiv_ind_cdvdelay: classderiv_ind_cdvdelay_compseq_tag_def,
cdvdelay-dummy: cdvdelay-dummy(x),
nth_tl: nth_tl(n;as),
firstn: firstn(n;as),
cdvpair: cdvpair(fst;snd),
it: 
,
cdvdelay: cdvdelay(X;dummy),
bfalse: ff,
btrue: tt,
unit: Unit,
union: left + right,
bool: 
,
let: let,
minus: -n,
subtract: n - m,
int_iseg: {i...j},
rev_implies: P Q,
squash: 
T
Lemmas :
append_firstn_lastn,
concat_append,
squash_wf,
map_append,
int_iseg_wf,
length_firstn,
rev_implies_wf,
iff_wf,
pos_length2,
length_nth_tl,
list-to-cdv_wf,
bool_wf,
eq_int_wf,
bnot_wf,
assert_of_eq_int,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
eqtt_to_assert,
listp_wf,
subtype_rel_wf,
nth_tl_wf,
cdvdelay_wf,
firstn_wf,
cdvpair_wf,
ge_wf,
le_wf,
not_wf,
pos_length3,
length-map,
cdv-types-non-empty,
top_wf,
member_wf,
concat-cons,
l_all_cons,
length_wf_nat,
concat_wf,
append_wf,
subtype_base_sq,
list_subtype_base,
non_neg_length,
cdv-types-list-to-cdv,
false_wf,
ifthenelse_wf,
true_wf,
assert_of_lt_int,
assert_wf,
lt_int_wf,
classderiv_wf,
cdv-wf_wf,
nat_wf,
l_member_wf,
cdv-types_wf,
length_wf1,
l_all_wf2,
l_all_wf,
int_seg_wf,
bag_wf,
select_wf,
map_wf,
hd_wf,
cdv-argtype_wf,
pack-cdv-args_wf
\mforall{}[L:\{dv:ClassDerivation| WF(dv)\} List]. \mforall{}[n:\mBbbN{}]. \mforall{}[m:\{m:\mBbbN{}| 0 < (n + m)\} ].
(cdv-argtype(pack-cdv-args(n;m;L))
= (k:\mBbbN{}||L|| {}\mrightarrow{} bag(map(\mlambda{}dv.hd(cdv-types(dv));L)[k]))) supposing
((||L|| = (n + m)) and
(\mforall{}dv\mmember{}L.||cdv-types(dv)|| = 1))
Date html generated:
2011_08_17-PM-04_32_34
Last ObjectModification:
2011_06_18-AM-11_43_42
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