Nuprl Lemma : disjoint-union-comb-classrel
[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)))
Proof not projected
Definitions occuring in Statement :
disjoint-union-comb: 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],
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-comb: X (+) Y,
squash: T,
or: P Q,
and: P Q,
assert: b,
isl: isl(x),
outl: outl(x),
outr: outr(x),
uimplies: b supposing a,
member: t T,
true: True,
prop: 
,
bag-member: x bs,
exists: 
x:A. B[x],
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
cand: A c B,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
not: A,
implies: P 
Q,
guard: {T},
bnot: 
b,
sq_or: a b,
uall: [x:A]. B[x],
all: x:A. B[x],
false: False,
so_apply: x[s],
so_apply: x[s1;s2],
sq_type: SQType(T),
sq_stable: SqStable(P),
rev_uimplies: rev_uimplies(P;Q),
subtype: S 
T
Lemmas :
classrel_wf,
parallel-class_wf,
simple-comb-1_wf,
lifting-1_wf,
squash_wf,
or_wf,
true_wf,
not_wf,
exists_wf,
and_wf,
equal_wf,
bag_wf,
bag_qinc,
l_member_wf,
false_wf,
disjoint-union-comb_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
parallel-classrel,
simple-comb-1-classrel,
assert_wf,
isl_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
not_assert_elim,
btrue_wf,
outl_wf,
outr_wf,
bnot_wf,
sq_stable__classrel
\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)))
Date html generated:
2012_01_23-PM-01_25_30
Last ObjectModification:
2012_01_11-AM-11_18_24
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