{ 
[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
((X |
Y))' = ((X)' | (Y)') supposing Singlevalued(X) 
Singlevalued(Y) }
{ Proof }
Definitions occuring in Statement :
es-or-latest: (X | Y),
es-prior-val: (X)',
es-interface-or: (X | Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
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 :
btrue: tt,
sq_type: SQType(T),
es-prior-interface: prior(X),
es-interface-at: X@i,
intensional-universe: IType,
eq_term: a == b,
valueall-type: valueall-type(T),
sqequal: s ~ t,
dataflow: dataflow(A;B),
b-union: A 
B,
fpf-cap: f(x)?z,
record: record(x.T[x]),
es-loc: loc(e),
bool: 
,
true: True,
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,
sq_stable: SqStable(P),
eclass-val: X(e),
es-pred: pred(e),
Id: Id,
int_seg: {i..j},
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A B,
cmp-le: cmp-le(cmp;x;y),
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
list: type List,
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
nat: 
,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
unit: Unit,
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
decidable: Dec(P),
so_apply: x[s],
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
infix_ap: x f y,
es-causl: (e < e'),
cand: A c B,
es-E-interface: E(X),
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_atom: eq_atom$n(x;y),
atom: Atom,
apply: f a,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
bag: bag(T),
rev_implies: P 
Q,
so_lambda: 
x.t[x],
implies: P 
Q,
union: left + right,
or: P 
Q,
es-locl: (e <loc e'),
exists: x:A. B[x],
subtype: S T,
event_ordering: EO,
lambda: x.A[x],
top: Top,
pair: <a, b>,
fpf: a:A fp-> B[a],
void: Void,
false: False,
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],
axiom: Ax,
one_or_both: one_or_both(A;B),
prop: 
,
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t T,
and: P Q,
product: x:A 
B[x],
so_lambda: x y.t[x; y],
sv-class: Singlevalued(X),
es-prior-val: (X)',
es-interface-or: (X | Y),
in-eclass: e 
X,
assert: 
b,
es-or-latest: (X | Y),
iff: P Q,
es-E: E,
all: x:A. B[x],
event-ordering+: EO+(Info),
cond-class: [X?Y],
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
one_or_both_ind_oobright: one_or_both_ind_oobright_compseq_tag_def,
oobright-rval: oobright-rval(x),
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),
natural_number: $n,
bag-size: bag-size(bs),
limited-type: LimitedType,
bfalse: ff,
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,
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: 
,
oob-apply: oob-apply(xs;ys),
eclass-compose2: eclass-compose2(f;X;Y),
es-latest-val: (X),
oobright: oobright(rval),
oobboth: oobboth(bval),
oobleft: oobleft(lval),
MaAuto: Error :MaAuto,
THEN: Error :THEN,
ParallelOp: Error :ParallelOp,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
bag-only: only(bs),
real: 
,
grp_car: |g|,
it: 
,
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor
Lemmas :
oobright_wf,
oobleft_wf,
bag_wf,
squash_wf,
set_subtype_base,
nat_wf,
bag-size_wf,
eq_int_wf,
assert_of_eq_int,
not_functionality_wrt_uiff,
bag-only_wf,
oobboth_wf,
es-le_wf,
is-latest-val,
or-latest-val,
interface-or-val,
es-latest-val_wf,
prior-val-as-latest-val,
prior-val-val,
product_subtype_base,
union_subtype_base,
es-prior-interface_wf1,
es-prior-interface_wf,
es-E-interface_wf,
not_wf,
bnot_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
le_wf,
es-interface-extensionality,
eclass-val_wf,
es-E_wf,
es-locl_wf,
assert_wf,
event-ordering+_wf,
all_functionality_wrt_iff,
iff_wf,
es-prior-val_wf,
one_or_both_wf,
es-or-latest_wf,
event-ordering+_inc,
eclass_wf,
sv-class_wf,
es-interface-or_wf,
iff_functionality_wrt_iff,
iff_transitivity,
is-prior-val,
exists_functionality_wrt_iff,
and_functionality_wrt_iff,
rev_implies_wf,
is-or-latest,
is-interface-or,
or_functionality_wrt_iff,
es-base-E_wf,
subtype_rel_self,
in-eclass_wf,
top_wf,
member_wf,
es-interface-top,
es-interface-subtype_rel2,
subtype_rel_wf,
es-causl_wf,
Id_wf,
sq_stable__assert,
bool_wf,
intensional-universe_wf,
decidable__assert,
false_wf,
ifthenelse_wf,
true_wf,
subtype_base_sq,
bool_subtype_base,
assert_elim
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
((X |\msupminus{} Y))' = ((X)' | (Y)') supposing Singlevalued(X) \mwedge{} Singlevalued(Y)
Date html generated:
2011_08_16-PM-06_10_19
Last ObjectModification:
2011_06_20-AM-01_48_45
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