Nuprl Lemma : disjoint-union-classrel
[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E].
v:A + B. uiff(v 
X + Y(e);case v of inl(x) => x X(e) | inr(x) => x 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,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
all: x:A. B[x],
not: A,
and: P Q,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
uiff: uiff(P;Q),
classrel: v X(e),
disjoint-union-class: X + Y,
and: P Q,
uimplies: b supposing a,
member: t T,
bag-member: bag-member(T;x;bs),
squash: 
T,
true: True,
prop: 
,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
not: A,
bnot: 
b,
bfalse: ff,
btrue: tt,
sq_stable: SqStable(P),
implies: P 
Q,
guard: {T},
assert: 
b,
outl: outl(x),
isl: isl(x),
false: False,
so_lambda: x.t[x],
outr: outr(x),
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],
so_apply: x[s1;s2],
or: P 
Q,
sq_type: SQType(T),
so_apply: x[s],
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,
not_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
sq_stable__classrel,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
uiff_transitivity,
assert_wf,
empty-bag_wf,
eqtt_to_assert,
assert-bag-null,
bag-member-map,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
outl_wf,
isl_wf,
squash_wf,
sq_stable__and,
sq_stable__all,
sq_stable__not,
outr_wf,
bag-member_wf,
bag-member-empty-iff,
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);case v of inl(x) => x \mmember{} X(e) | inr(x) => x \mmember{} Y(e) \mwedge{} (\mforall{}w:A. (\mneg{}w \mmember{} X(e))))
Date html generated:
2011_10_20-PM-03_38_15
Last ObjectModification:
2011_09_23-PM-11_20_25
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