{ 
[Info,A1,A2,B:Type]. [P1:A1 
]. [P2:A2 ]. [f1:A1 B].
[f2:A2 B]. [X1:EClass(A1)]. [X2:EClass(A2)].
(f1[v] where v from X1 such that P1[v])
= (f2[v] where v from X2 such that P2[v])
supposing es:EO+(Info). e:E.
((
e 
X1 
e X2)
((e X1)
(e X2)
((P1[X1(e)] P2[X2(e)])
((P1[X1(e)])
(P2[X2(e)])
(f1[X1(e)] = f2[X2(e)]))))) }
{ Proof }
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
implies: P Q,
and: P Q,
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
rev_uimplies: rev_uimplies(P;Q),
intensional-universe: IType,
eq_term: a == b,
valueall-type: valueall-type(T),
sqequal: s ~ t,
tag-by: z
T,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
fpf-cap: f(x)?z,
record: record(x.T[x]),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x 
y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f 
g,
squash: 
T,
cond-class: [X?Y],
void: Void,
true: True,
false: False,
sv-class: Singlevalued(X),
cand: A c B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
sq_stable: SqStable(P),
union: left + right,
or: P 
Q,
guard: {T},
eq_knd: a = b,
list: type List,
l_member: (x l),
fpf-dom: x dom(f),
bag: bag(T),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
dep-isect: Error :dep-isect,
record+: record+,
limited-type: LimitedType,
lambda: 
x.A[x],
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e X,
subtype: S T,
top: Top,
so_lambda: 
x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
rev_implies: P Q,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
axiom: Ax,
apply: f a,
so_apply: x[s],
mapfilter-class: (f[v] where v from X such that P[v]),
prop: 
,
event-ordering+: EO+(Info),
event_ordering: EO,
es-E: E,
iff: P Q,
assert: b,
implies: P Q,
product: x:A B[x],
and: P Q,
all: x:A. B[x],
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
equal: s = t,
universe: Type,
bool: ,
uall: [x:A]. B[x],
isect: x:A. B[x],
member: t T,
function: x:A B[x],
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
THENM: Error :THENM,
Try: Error :Try,
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
natural_number: $n,
bag-size: bag-size(bs),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
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'),
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',
bimplies: p q,
band: p q,
bor: p q,
bnot: b,
int: 
,
unit: Unit,
eclass-compose1: f o X,
es-filter-image: f[X],
Auto: Error :Auto
Lemmas :
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
not_wf,
assert_wf,
eclass_wf,
event-ordering+_wf,
es-E_wf,
iff_wf,
bool_wf,
mapfilter-class_wf,
event-ordering+_inc,
in-eclass_wf,
eclass-val_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
uall_wf,
es-base-E_wf,
subtype_rel_self,
es-interface-extensionality,
sv-class_wf,
le_wf,
false_wf,
ifthenelse_wf,
true_wf,
top_wf,
rev_implies_wf,
sq_stable__assert,
intensional-universe_wf,
is-mapfilter-class,
mapfilter-class-val
\mforall{}[Info,A1,A2,B:Type]. \mforall{}[P1:A1 {}\mrightarrow{} \mBbbB{}]. \mforall{}[P2:A2 {}\mrightarrow{} \mBbbB{}]. \mforall{}[f1:A1 {}\mrightarrow{} B]. \mforall{}[f2:A2 {}\mrightarrow{} B]. \mforall{}[X1:EClass(A1)].
\mforall{}[X2:EClass(A2)].
(f1[v] where v from X1 such that P1[v]) = (f2[v] where v from X2 such that P2[v])
supposing \mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X1 \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} X2)
\mwedge{} ((\muparrow{}e \mmember{}\msubb{} X1)
{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X2)
{}\mRightarrow{} ((\muparrow{}P1[X1(e)] \mLeftarrow{}{}\mRightarrow{} \muparrow{}P2[X2(e)])
\mwedge{} ((\muparrow{}P1[X1(e)]) {}\mRightarrow{} (\muparrow{}P2[X2(e)]) {}\mRightarrow{} (f1[X1(e)] = f2[X2(e)])))))
Date html generated:
2011_08_16-PM-04_14_43
Last ObjectModification:
2011_06_20-AM-00_44_15
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