Nuprl Lemma : disjoint-union-classrel-ite
[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E]. [v:A + B].
uiff(v 
X + Y(e);
((
isl(v)) 
outl(v) X(e)) 
((
isl(v)) outr(v) Y(e) (w:A. (w X(e)))))
Proof not projected
Definitions occuring in Statement :
disjoint-union-class: X + Y,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
outr: outr(x),
outl: outl(x),
isl: isl(x),
assert: b,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
all: x:A. B[x],
not: A,
squash: T,
or: P Q,
and: P Q,
union: left + right,
universe: Type
Definitions :
uiff: uiff(P;Q),
classrel: v X(e),
disjoint-union-class: X + Y,
squash: T,
or: P Q,
and: P Q,
assert: b,
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
member: t T,
true: True,
prop: 
,
bag-member: bag-member(T;x;bs),
cand: A c B,
bnot: 
b,
btrue: tt,
bfalse: ff,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
isl: isl(x),
outl: outl(x),
not: A,
outr: outr(x),
implies: P 
Q,
guard: {T},
false: False,
simple-comb-2: F|X, Y|,
simple-comb: simple-comb(F;Xs),
select: l[i],
le_int: i 
z j,
lt_int: i <z j,
exists: 
x:A. B[x],
uall: [x:A]. B[x],
sq_type: SQType(T),
so_apply: x[s1;s2],
sq_stable: SqStable(P),
bool: 
,
unit: Unit,
rev_uimplies: rev_uimplies(P;Q),
subtype: S 
T,
it: 
Lemmas :
classrel_wf,
simple-comb-2_wf,
ifthenelse_wf,
bag-null_wf,
bag_wf,
bag-map_wf,
squash_wf,
assert_wf,
isl_wf,
outl_wf,
not_wf,
outr_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
not_assert_elim,
btrue_wf,
disjoint-union-class_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
bnot_wf,
bool_cases,
uiff_transitivity,
empty-bag_wf,
eqtt_to_assert,
assert-bag-null,
bag-member-map,
false_wf,
bag-member_wf,
bag-member-empty-iff,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
true_wf,
sq_stable__classrel,
empty-bag-iff-no-member
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A + B].
uiff(v \mmember{} X + Y(e);\mdownarrow{}((\muparrow{}isl(v)) \mwedge{} outl(v) \mmember{} X(e))
\mvee{} ((\mneg{}\muparrow{}isl(v)) \mwedge{} outr(v) \mmember{} Y(e) \mwedge{} (\mforall{}w:A. (\mneg{}w \mmember{} X(e)))))
Date html generated:
2011_10_20-PM-03_38_29
Last ObjectModification:
2011_09_26-PM-07_13_14
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