Nuprl Lemma : State-class-single-val

∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(B)].

  (single-valued-classrel(es;State-class(init;f;X);B)) supposing
     ((∀l:Id. single-valued-bag(init l;B)) and
     single-valued-classrel(es;X;A))

Proof

Definitions occuring in Statement : State-class: State-class(init;f;X), 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], all: ∀x:A. B[x], apply: f a, function: x:A ─→ B[x], universe: Type, single-valued-bag: single-valued-bag(b;T), bag: bag(T)
Lemmas : State-class-single-val0, classrel_wf, State-class_wf, es-E_wf, event-ordering+_subtype, es-loc_wf, all_wf, Id_wf, single-valued-bag_wf, single-valued-classrel_wf, bag_wf, eclass_wf, event-ordering+_wf

Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. (single-valued-classrel(es;State-class(init;f;X);B)) supposing ((\mforall{}l:Id. single-valued-bag(init l;B)) and single-valued-classrel(es;X;A)) Date html generated: 2015_07_22-PM-00_20_25 Last ObjectModification: 2015_01_28-AM-10_13_27 Home Index