{ 
[B:Type]. [n:
]. [m:n + 1]. [A:n 
Type]. [bags:k:n bag(A k)].
[g:funtype(n - m;
x.(A (x + m));B)].
(lifting-gen-list-rev(n;bags) m g 
bag(B)) }
{ Proof }
Definitions occuring in Statement :
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
int_seg: {i..j
},
nat: ,
uall: [x:A]. B[x],
member: t T,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
bag: bag(T),
funtype: funtype(n;A;T)
Definitions :
apply: f a,
funtype: funtype(n;A;T),
universe: Type,
prop: 
,
bag: bag(T),
member: t T,
so_lambda: 
x.t[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
int_seg: {i..j},
function: x:A B[x],
lifting-gen-list-rev: Error :lifting-gen-list-rev,
axiom: Ax,
lambda: x.A[x],
add: n + m,
bool: 
,
natural_number: $n,
set: {x:A| B[x]} ,
all: x:A. B[x],
subtype: S 
T,
rationals: 
,
real: 
,
le: A 
B,
not: 
A,
false: False,
implies: P 
Q,
void: Void,
less_than: a < b,
minus: -n,
lelt: i j < k,
and: P 
Q,
subtype_rel: A r B,
uiff: uiff(P;Q),
product: x:A 
B[x],
uimplies: b supposing a,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
grp_car: |g|,
limited-type: LimitedType,
subtract: n - m,
int: 
,
equal: s = t,
nat: ,
exists: 
x:A. B[x],
sq_type: SQType(T),
guard: {T},
iff: P 
Q,
rev_implies: P Q,
label: ...$L... t,
sqequal: s ~ t,
ycomb: Y,
top: Top,
union: left + right,
unit: Unit,
bnot: 
b,
assert: 
b,
eq_int: (i =
j),
bor: p 
q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_atom: x =a y,
btrue: tt,
bfalse: ff,
le_int: i z j,
lt_int: i <z j,
single-bag: {x},
primrec: primrec(n;b;c),
fpf: a:A fp-> B[a],
eclass: EClass(A[eo; e]),
bag-combine: 
xbs.f[x],
intensional-universe: IType,
l_member: (x l),
or: P Q,
so_apply: x[s],
ifthenelse: if b then t else f fi ,
fpf-cap: f(x)?z,
pair: <a, b>,
squash: 
T,
true: True
Lemmas :
squash_wf,
true_wf,
subtype_rel-equal,
primrec_wf,
bool_subtype_base,
bool_cases,
intensional-universe_wf,
bag-combine_wf,
single-bag_wf,
eq_int_wf,
bnot_wf,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert_wf,
assert_of_eq_int,
eqtt_to_assert,
uiff_transitivity,
bool_wf,
ycomb-unroll,
ge_wf,
subtype_rel_wf,
nat_ind_tp,
rev_implies_wf,
iff_wf,
int_subtype_base,
subtype_base_sq,
uall_wf,
bag_wf,
funtype_wf,
nat_properties,
int_seg_properties,
int_seg_wf,
nat_wf,
member_wf,
le_wf,
not_wf,
false_wf
\mforall{}[B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[m:\mBbbN{}n + 1]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[bags:k:\mBbbN{}n {}\mrightarrow{} bag(A k)].
\mforall{}[g:funtype(n - m;\mlambda{}x.(A (x + m));B)].
(lifting-gen-list-rev(n;bags) m g \mmember{} bag(B))
Date html generated:
2011_08_17-PM-05_58_18
Last ObjectModification:
2011_06_22-AM-11_30_21
Home
Index