{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
[e:E].
(X | Y)(e)
= if e 
X
then if e Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi
else oobright(Y(e))
fi
supposing 
e (X | Y) }
{ Proof }
Definitions occuring in Statement :
es-interface-or: (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],
pair: <a, b>,
universe: Type,
equal: s = t,
oobright: oobright(rval),
oobleft: oobleft(lval),
oobboth: oobboth(bval),
one_or_both: one_or_both(A;B)
Definitions :
implies: P 
Q,
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
axiom: Ax,
oobright: Error :oobright,
oobleft: Error :oobleft,
pair: <a, b>,
oobboth: Error :oobboth,
eclass-val: X(e),
void: Void,
es-E-interface: E(X),
quotient: x,y:A//B[x; y],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
one_or_both: Error :one_or_both,
es-interface-or: (X | Y),
in-eclass: e X,
set: {x:A| B[x]} ,
prop: 
,
assert: b,
uimplies: b supposing a,
bag: bag(T),
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A 
B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
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),
empty-bag: {},
bag-only: only(bs),
single-bag: {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,
bag-size: bag-size(bs),
eq_int: (i =
j),
bnot: b,
int: 
,
unit: Unit,
union: left + right,
bool: 
,
oob-apply: oob-apply(xs;ys),
eclass-compose2: eclass-compose2(f;X;Y),
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor,
Auto: Error :Auto,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
bag_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,
bag-only_wf,
single-bag_wf,
Error :oobleft_wf,
true_wf,
Error :oobright_wf,
false_wf,
eclass-val_wf,
es-interface-or_wf,
Error :one_or_both_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
top_wf,
subtype_rel_wf,
es-interface-subtype_rel2,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
assert_wf,
Error :oobboth_wf,
ifthenelse_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 if e \mmember{}\msubb{} Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi
else oobright(Y(e))
fi
supposing \muparrow{}e \mmember{}\msubb{} (X | Y)
Date html generated:
2011_08_16-PM-04_23_07
Last ObjectModification:
2011_06_20-AM-00_48_59
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