Nuprl Lemma : simple-loc-comb-3-concat-single-val
[Info:Type]. [es:EO+(Info)]. [A,B,C,D:Type]. [F:Id 
A B C bag(D)]. [X:EClass(A)]. [Y:EClass(B)].
[Z:EClass(C)].
single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D)
supposing (i:Id. a:A. b:B. c:C. (bag-size(F i a b c) 
1))
single-valued-classrel(es;X;A)
single-valued-classrel(es;Y;B)
single-valued-classrel(es;Z;C)
Proof not projected
Definitions occuring in Statement :
concat-lifting-loc-3: concat-lifting-loc-3(f),
simple-loc-comb-3: F|Loc, X, Y, Z|,
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: [x:A]. B[x],
le: A B,
all: x:A. B[x],
and: P Q,
apply: f a,
function: x:A B[x],
natural_number: $n,
universe: Type,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
eclass: EClass(A[eo; e]),
and: P Q,
all: x:A. B[x],
single-valued-classrel: single-valued-classrel(es;X;T),
implies: P 
Q,
member: t 
T,
prop: 
,
cand: A c B,
so_lambda: 
x.t[x],
uall: [x:A]. B[x],
uimplies: b supposing a,
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
select: l[i],
ycomb: Y,
ifthenelse: if b then t else f fi ,
eq_int: (i =
j),
btrue: tt,
bfalse: ff,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
le: A B,
or: P 
Q,
not: A,
false: False,
iff: P 
Q,
squash: 
T,
true: True,
rev_implies: P Q,
classrel: v X(e),
simple-loc-comb-3: F|Loc, X, Y, Z|,
concat-lifting-loc-3: concat-lifting-loc-3(f),
simple-loc-comb: F|Loc; Xs|,
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
uiff: uiff(P;Q),
so_apply: x[s],
nat: 
,
exists: 
x:A. B[x],
subtype: S 
T
Lemmas :
bag-member-union,
classrel_wf,
simple-loc-comb-3_wf,
concat-lifting-loc-3_wf,
es-E_wf,
event-ordering+_inc,
all_wf,
Id_wf,
le_wf,
bag-size_wf,
nat_wf,
implies-wf,
equal_wf,
event-ordering+_wf,
bag_wf,
bag-combine_wf,
single-bag_wf,
es-loc_wf,
bag-member-combine,
bag-member-single,
bag-size-zero,
bag-member_wf,
squash_wf,
true_wf,
bag-member-empty-iff,
bag-size-one,
bag-only_wf,
and_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C,D:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C {}\mrightarrow{} bag(D)]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)].
single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D)
supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. \mforall{}c:C. (bag-size(F i a b c) \mleq{} 1))
\mwedge{} single-valued-classrel(es;X;A)
\mwedge{} single-valued-classrel(es;Y;B)
\mwedge{} single-valued-classrel(es;Z;C)
Date html generated:
2012_01_23-PM-01_15_20
Last ObjectModification:
2011_11_11-AM-11_22_30
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