{ 
[Info,T,S:Type]. [X,Y:EClass(T)]. [Z:T 
EClass(S)].
(X || Y >t> Z[t] = X >t> Z[t] || Y >t> Z[t]) }
{ Proof }
Definitions occuring in Statement :
parallel-class: X || Y,
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
atom_eq: atomeqn def,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sq_type: SQType(T),
sqequal: s ~ t,
rationals: 
,
append: as @ bs,
guard: {T},
locl: locl(a),
Knd: Knd,
atom: Atom$n,
l_member: (x 
l),
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),
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
valueall-type: valueall-type(T),
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),
squash: 
T,
sq_stable: SqStable(P),
limited-type: LimitedType,
es-locl: (e <loc e'),
es-loc: loc(e),
Id: Id,
bool: 
,
record-update: r[x := v],
eo-restrict: eo-restrict(eo;P),
eo-forward: eo.e,
bag-combine: 
xbs.f[x],
bag-append: as + bs,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
nil: [],
tag-by: z
T,
rev_implies: P 
Q,
or: P 
Q,
implies: P 
Q,
iff: P Q,
record: record(x.T[x]),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A B,
union: left + right,
true: True,
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
prop: 
,
class-program: ClassProgram(T),
fpf-cap: f(x)?z,
atom: Atom,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
assert: 
b,
record-select: r.x,
eclass-compose2: eclass-compose2(f;X;Y),
subtype: S T,
event_ordering: EO,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
so_lambda: 
x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
axiom: Ax,
apply: f a,
so_apply: x[s],
parallel-class: X || Y,
bind-class: X >x> Y[x],
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
function: x:A B[x],
isect: x:A. B[x],
MaAuto: Error :MaAuto,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
ORELSE: Error :ORELSE,
es-le: e loc e' ,
es-E: E,
set: {x:A| B[x]} ,
list: type List,
es-le-before: loc(e),
bag: bag(T),
member: t T,
AssertBY: Error :AssertBY,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
RepUR: Error :RepUR
Lemmas :
es-le_wf,
subtype_rel_wf,
bag_wf,
es-E_wf,
subtype_rel_self,
es-base-E_wf,
es-le-before_wf2,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
parallel-class_wf,
member_wf,
permutation_wf,
bag-combine_wf,
iff_wf,
rev_implies_wf,
bag-combine-append-right,
bag-append_wf,
eo-forward_wf,
member-eo-forward-E,
Id_wf,
es-locl_wf,
es-loc_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__es-le,
assert_wf,
uiff_wf,
assert-eq-id,
subtype_base_sq,
true_wf,
squash_wf,
bag-combine-append-left
\mforall{}[Info,T,S:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[Z:T {}\mrightarrow{} EClass(S)].
(X || Y >t> Z[t] = X >t> Z[t] || Y >t> Z[t])
Date html generated:
2011_08_16-AM-11_37_34
Last ObjectModification:
2011_06_20-AM-00_30_10
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