{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [P:A 
]. [f:A B].
[X:EClass(A)]. [e:E].
(f[v] where v from X such that P[v])(e) ~ f[X(e)]
supposing 
e 
(f[v] where v from X such that P[v]) }
{ 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],
function: x:A B[x],
universe: Type,
sqequal: s ~ t
Definitions :
true: True,
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
eq_bool: p =b q,
strong-subtype: strong-subtype(A;B),
record-select: r.x,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
less_than: a < b,
sq_type: SQType(T),
subtype_rel: A 
r B,
bag: bag(T),
empty-bag: {},
single-bag: {x},
bag-only: only(bs),
ifthenelse: if b then t else f fi ,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
false: False,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
nat: 
,
limited-type: LimitedType,
btrue: tt,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
eq_atom: x =a y,
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'),
not: 
A,
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',
bimplies: p 
q,
band: p q,
bor: p 
q,
natural_number: $n,
bag-size: bag-size(bs),
eq_int: (i =
j),
bnot: b,
int: 
,
unit: Unit,
union: left + right,
eclass-val: X(e),
eclass-compose1: f o X,
es-filter-image: f[X],
implies: P Q,
subtype: S T,
void: Void,
lambda: 
x.A[x],
top: Top,
apply: f a,
so_apply: x[s],
so_lambda: 
x.t[x],
mapfilter-class: (f[v] where v from X such that P[v]),
all: x:A. B[x],
in-eclass: e X,
equal: s = t,
prop: 
,
assert: b,
event_ordering: EO,
es-E: E,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
sqequal: s ~ t,
event-ordering+: EO+(Info),
universe: Type,
bool: ,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
function: x:A B[x],
member: t T,
Repeat: Error :Repeat,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
Unfold: Error :Unfold,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic
Lemmas :
nat_wf,
bag-size_wf,
eq_int_wf,
assert_wf,
not_wf,
bnot_wf,
bool_wf,
assert_of_eq_int,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
eqtt_to_assert,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass_wf,
top_wf,
mapfilter-class_wf,
in-eclass_wf,
single-bag_wf,
bag_wf,
ifthenelse_wf,
bag-only_wf,
subtype_base_sq,
empty-bag_wf,
false_wf,
true_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(f[v] where v from X such that P[v])(e) \msim{} f[X(e)]
supposing \muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v])
Date html generated:
2011_08_16-PM-04_14_25
Last ObjectModification:
2011_06_20-AM-00_44_08
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