{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
[e:E].
(X |
Y)(e) = ((X) | (Y))(e)
supposing (
e 
(X | Y)) 
Singlevalued(X) Singlevalued(Y) }
{ Proof }
Definitions occuring in Statement :
es-or-latest: (X | Y),
es-latest-val: (X),
es-interface-or: (X | Y),
sv-class: Singlevalued(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
and: P Q,
universe: Type,
equal: s = t,
one_or_both: one_or_both(A;B)
Definitions :
iff: P 
Q,
bool: 
,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-E-interface: E(X),
cand: A c B,
apply: f a,
so_apply: x[s],
implies: P Q,
or: P 
Q,
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
bag: bag(T),
so_lambda: 
x.t[x],
union: left + right,
subtype: S 
T,
lambda: x.A[x],
top: Top,
in-eclass: e X,
pair: <a, b>,
fpf: a:A fp-> B[a],
void: Void,
false: False,
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
record+: record+,
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,
function: x:A 
B[x],
all: x:A. B[x],
axiom: Ax,
es-latest-val: (X),
es-interface-or: (X | Y),
es-or-latest: (X | Y),
eclass-val: X(e),
one_or_both: one_or_both(A;B),
prop: 
,
assert: b,
sv-class: Singlevalued(X),
product: x:A 
B[x],
and: P Q,
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],
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
empty-bag: {},
one_or_both_ind_oobright: one_or_both_ind_oobright_compseq_tag_def,
oobright-rval: oobright-rval(x),
inl: inl x ,
inr: inr x ,
single-bag: {x},
bag-only: only(bs),
one_or_both_ind_oobleft: one_or_both_ind_oobleft_compseq_tag_def,
oobleft-lval: oobleft-lval(x),
oobboth?: oobboth?(x),
oobleft?: oobleft?(x),
oobright?: oobright?(x),
one_or_both_ind_oobboth: one_or_both_ind_oobboth_compseq_tag_def,
oobboth-bval: oobboth-bval(x),
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),
limited-type: LimitedType,
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,
oob-apply: oob-apply(xs;ys),
primed-class: Prior(X),
es-interface-union: X+Y,
latest-pair: (X&Y),
eclass-compose2: eclass-compose2(f;X;Y),
eclass-compose4: eclass-compose4(f;X;Y;Z;V),
es-prior-val: (X)',
oobboth: oobboth(bval),
squash: 
T,
true: True,
so_apply: x[s1;s2],
sq_type: SQType(T),
sqequal: s ~ t,
oobleft: oobleft(lval),
oobright: oobright(rval)
Lemmas :
oobright_wf,
oobleft_wf,
false_wf,
ifthenelse_wf,
subtype_base_sq,
primed-class-prior-val,
squash_wf,
true_wf,
es-prior-val_wf,
primed-class_wf,
oobboth_wf,
not_wf,
bnot_wf,
bool_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
es-latest-val_wf,
eclass-val_wf,
es-or-latest_wf,
es-interface-or_wf,
one_or_both_wf,
assert_wf,
sv-class_wf,
es-E_wf,
eclass_wf,
event-ordering+_wf,
in-eclass_wf,
event-ordering+_inc,
member_wf,
subtype_rel_wf,
es-interface-top,
uall_wf,
es-interface-subtype_rel2,
es-base-E_wf,
subtype_rel_self,
top_wf,
is-or-latest
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
(X |\msupminus{} Y)(e) = ((X)\msupminus{} | (Y)\msupminus{})(e) supposing (\muparrow{}e \mmember{}\msubb{} (X |\msupminus{} Y)) \mwedge{} Singlevalued(X) \mwedge{} Singlevalued(Y)
Date html generated:
2011_08_16-PM-06_06_19
Last ObjectModification:
2011_06_20-AM-01_47_52
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