Nuprl Lemma : simple-comb-classrel
[Info,B:Type]. [n:
]. [A:n 
Type]. [Xs:k:n EClass(A k)]. [f:k:n (A k) B].
[F:k:n bag(A k) bag(B)].
[es:EO+(Info)]. [e:E]. [v:B].
uiff(v 
simple-comb(F;Xs)(e);
vs:k:n (A k). ((k:n. vs[k] Xs[k](e)) 
(v = (f vs))))
supposing v:B. bs:k:n bag(A k). (v F bs 
vs:k:n (A k). ((k:n. vs k bs k) (v = (f vs))))
Proof not projected
Definitions occuring in Statement :
simple-comb: simple-comb(F;Xs),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
int_seg: {i..j
},
nat: ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
squash: T,
and: P Q,
apply: f a,
function: x:A B[x],
natural_number: $n,
universe: Type,
equal: s = t,
bag-member: x bs,
bag: bag(T)
Definitions :
bag-member: x bs,
squash: T,
and: P Q,
uiff: uiff(P;Q),
classrel: v X(e),
so_apply: x[s],
uimplies: b supposing a,
member: t T,
true: True,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
all: x:A. B[x],
exists: x:A. B[x],
simple-comb: simple-comb(F;Xs),
prop: 
,
cand: A c B,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
iff: P Q,
implies: P Q,
sq_stable: SqStable(P),
rev_implies: P Q,
subtype: S 
T,
eclass: EClass(A[eo; e]),
guard: {T}
Lemmas :
classrel_wf,
simple-comb_wf,
squash_wf,
exists_wf,
and_wf,
all_wf,
equal_wf,
int_seg_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
bag_wf,
iff_wf,
bag-member_wf,
eclass_wf,
nat_wf,
sq_stable__bag-member
\mforall{}[Info,B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[Xs:k:\mBbbN{}n {}\mrightarrow{} EClass(A k)]. \mforall{}[f:k:\mBbbN{}n {}\mrightarrow{} (A k) {}\mrightarrow{} B].
\mforall{}[F:k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:B].
uiff(v \mmember{} simple-comb(F;Xs)(e);\mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. vs[k] \mmember{} Xs[k](e)) \mwedge{} (v = (f vs))))
supposing \mforall{}v:B. \mforall{}bs:k:\mBbbN{}n {}\mrightarrow{} bag(A k).
(v \mdownarrow{}\mmember{} F bs \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. vs k \mdownarrow{}\mmember{} bs k) \mwedge{} (v = (f vs))))
Date html generated:
2012_01_23-PM-01_09_35
Last ObjectModification:
2011_12_30-PM-08_20_46
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