Nuprl Lemma : rec-combined-loc-class-opt-1-single-val0

[Info,A,B:Type].

[es:EO+(Info)].

[F:Id

A

B

B].

[X:EClass(A)].

[init:Id

bag(B)].

[e:E].

[v1,v2:B].
(v1 = v2) supposing
(v1

lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
v2

lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))

Proof not projected

Definitions occuring in Statement : lifting-loc-2: lifting-loc-2(f), rec-combined-loc-class-opt-1: F|Loc, X, Prior(self)?init|, single-valued-classrel: single-valued-classrel(es;X;T), classrel: v

X(e), eclass: EClass(A[eo; e]), event-ordering+: EO+(Info), es-loc: loc(e), es-E: E, Id: Id, uimplies: b supposing a, uall:

[x:A]. B[x], apply: f a, function: x:A

B[x], universe: Type, equal: s = t, single-valued-bag: single-valued-bag(b;T), bag: bag(T)
Definitions : so_lambda:

x y.t[x; y], iff: P

Q, rev_implies: P

Q, and: P

Q, top: Top, true: True, squash:

T, false: False, not:

A, le: A

B, ge: i

j , nat:

, exists:

x:A. B[x], member: t

T, all:

x:A. B[x], implies: P

Q, so_apply: x[s1;s2], es-locl: (e <loc e'), es-p-local-pred: es-p-local-pred(es;P), or: P

Q, uiff: uiff(P;Q), uimplies: b supposing a, prop:

, uall:

[x:A]. B[x], strongwellfounded: SWellFounded(R[x; y]), single-valued-classrel: single-valued-classrel(es;X;T), single-valued-bag: single-valued-bag(b;T), subtype: S

T, guard: {T}
Lemmas : and_wf, event-ordering+_wf, eclass_wf, bag_wf, Id_wf, es-E_wf, event-ordering+_inc, es-loc_wf, single-valued-bag_wf, single-valued-classrel_wf, equal_wf, lifting-loc-2_wf, rec-combined-loc-class-opt-1_wf, classrel_wf, es-locl-trichotomy, primed-class-opt-classrel, primed-class-opt_wf, simple-loc-comb-2-classrel, rec-combined-loc-class-opt-1-classrel, es-causl_wf, le_wf, nat_wf, less_than_wf, ge_wf, nat_properties, es-causl-swellfnd

\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[e:E]. \mforall{}[v1,v2:B]. (v1 = v2) supposing (v1 \mmember{} lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and v2 \mmember{} lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and single-valued-classrel(es;X;A) and single-valued-bag(init loc(e);B)) Date html generated: 2012_02_20-PM-02_57_48 Last ObjectModification: 2012_02_07-PM-12_45_42 Home Index