{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
[e:E].
X+Y(e) = if e 
X then inl X(e) else inr Y(e) fi supposing 
e X+Y }
{ Proof }
Definitions occuring in Statement :
es-interface-union: X+Y,
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: [x:A]. B[x],
inr: inr x ,
inl: inl x ,
union: left + right,
universe: Type,
equal: s = t
Definitions :
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-E-interface: E(X),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
void: Void,
empty-bag: {},
single-bag: {x},
bag-only: only(bs),
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),
false: False,
lt_int: i <z j,
le_int: i 
z j,
bfalse: ff,
real: 
,
grp_car: |g|,
nat: 
,
limited-type: LimitedType,
btrue: tt,
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,
natural_number: $n,
apply: f a,
bag-size: bag-size(bs),
eq_int: (i =
j),
bnot: 
b,
int: 
,
unit: Unit,
bool: 
,
eclass-compose2: eclass-compose2(f;X;Y),
implies: P Q,
fpf-dom: x dom(f),
lambda: 
x.A[x],
subtype: S 
T,
quotient: x,y:A//B[x; y],
bag: bag(T),
top: Top,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[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 ,
not: A,
less_than: a < b,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
function: x:A 
B[x],
all: x:A. B[x],
axiom: Ax,
inr: inr x ,
inl: inl x ,
in-eclass: e X,
ifthenelse: if b then t else f fi ,
es-interface-union: X+Y,
eclass-val: X(e),
union: left + right,
prop: 
,
assert: b,
event_ordering: EO,
es-E: E,
uimplies: b supposing a,
equal: s = t,
event-ordering+: EO+(Info),
universe: Type,
uall: [x:A]. B[x],
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
member: t T,
isect: 
x:A. B[x],
RepeatFor: Error :RepeatFor,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Auto: Error :Auto,
tactic: Error :tactic
Lemmas :
es-interface-union_wf,
in-eclass_wf,
assert_wf,
event-ordering+_inc,
es-E_wf,
es-interface-top,
subtype_rel_wf,
eclass_wf,
member_wf,
eclass-val_wf,
event-ordering+_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
bag-size_wf,
nat_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
eq_int_wf,
true_wf,
bag-only_wf,
false_wf,
es-interface-subtype_rel2,
es-base-E_wf,
subtype_rel_self,
top_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
X+Y(e) = if e \mmember{}\msubb{} X then inl X(e) else inr Y(e) fi supposing \muparrow{}e \mmember{}\msubb{} X+Y
Date html generated:
2011_08_16-PM-04_20_31
Last ObjectModification:
2011_06_20-AM-00_48_38
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