Nuprl Lemma : simple-comb-2-concat-classrel
[Info,A,B,C:Type]. [f:A 
B bag(C)]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E]. [v:C].
uiff(v 
f@|X, Y|(e);
a:A. b:B. (a X(e) 
b Y(e) v f a b))
Proof not projected
Definitions occuring in Statement :
simple-comb-2: F|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],
exists: x:A. B[x],
squash: T,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
concat-lifting-2: f@,
bag-member: x bs,
bag: bag(T)
Definitions :
simple-comb-2: F|X, Y|,
concat-lifting-2: f@,
and: P Q,
select: l[i],
member: t T,
nat: 
,
int_seg: {i..j
},
le: A 
B,
not: 
A,
implies: P 
Q,
false: False,
so_lambda: 
x.t[x],
lelt: i j < k,
ifthenelse: if b then t else f fi ,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
so_lambda: x y.t[x; y],
uall: [x:A]. B[x],
uiff: uiff(P;Q),
classrel: v X(e),
squash: T,
bag-member: x bs,
uimplies: b supposing a,
true: True,
simple-comb2: x,y.F[x; y]|X;Y|,
prop: 
,
decidable: Dec(P),
all: x:A. B[x],
or: P 
Q,
sq_type: SQType(T),
guard: {T},
so_apply: x[s1;s2],
so_apply: x[s],
subtype: S 
T
Lemmas :
simple-comb2-concat-classrel,
classrel_wf,
simple-comb_wf,
le_wf,
select_wf,
length_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
int_seg_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
eclass_wf,
es-E_wf,
event-ordering+_inc,
concat-lifting2_wf,
lelt_wf,
bag_wf,
squash_wf,
exists_wf,
and_wf,
bag-member_wf,
event-ordering+_wf
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:C].
uiff(v \mmember{} f@|X, Y|(e);\mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Y(e) \mwedge{} v \mdownarrow{}\mmember{} f a b))
Date html generated:
2012_01_23-PM-01_11_06
Last ObjectModification:
2011_12_31-AM-01_53_20
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