Nuprl Lemma : simple-loc-comb-2-concat-single-val

[Info:Type].

[es:EO+(Info)].

[A,B,C:Type].

[F:Id

A

B

bag(C)].

[X:EClass(A)].

[Y:EClass(B)].
single-valued-classrel(es;F@Loc|Loc,X, Y|;C)
supposing (

i:Id.

a:A.

b:B. (bag-size(F i a b)

1))

single-valued-classrel(es;X;A)

single-valued-classrel(es;Y;B)

Proof not projected

Definitions occuring in Statement : concat-lifting-loc-2: f@Loc, simple-loc-comb-2: F|Loc,X, Y|, 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], le: A

B, single-valued-classrel: single-valued-classrel(es;X;T), implies: P

Q, squash:

T, member: t

T, true: True, or: P

Q, not:

A, false: False, iff: P

Q, prop:

, rev_implies: P

Q, cand: A c

B, so_lambda:

x.t[x], uall:

[x:A]. B[x], uimplies: b supposing a, exists:

x:A. B[x], uiff: uiff(P;Q), nat:

, so_apply: x[s], subtype: S

T
Lemmas : simple-loc-comb-2-concat-classrel, es-loc_wf, event-ordering+_inc, bag-size_wf, nat_wf, bag-size-zero, bag-member-empty-iff, bag-size-one, squash_wf, true_wf, bag_wf, bag-member-single, bag-only_wf, classrel_wf, simple-loc-comb-2_wf, concat-lifting-loc-2_wf, es-E_wf, all_wf, Id_wf, le_wf, implies-wf, equal_wf, event-ordering+_wf, and_wf

\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. single-valued-classrel(es;F@Loc|Loc,X, Y|;C) supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. (bag-size(F i a b) \mleq{} 1)) \mwedge{} single-valued-classrel(es;X;A) \mwedge{} single-valued-classrel(es;Y;B) Date html generated: 2012_01_23-PM-01_15_58 Last ObjectModification: 2011_11_11-PM-07_28_30 Home Index