Nuprl Lemma : State-comb-total

[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
  es-total-class(es;State-comb(init;f;X)) supposing ∀l:Id. (1 ≤ #(init l))


Proof




Definitions occuring in Statement :  State-comb: State-comb(init;f;X) es-total-class: es-total-class(es;X) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) Id: Id uimplies: supposing a uall: [x:A]. B[x] le: A ≤ B all: x:A. B[x] apply: a function: x:A ─→ B[x] natural_number: $n universe: Type bag-size: #(bs) bag: bag(T)
Lemmas :  State-comb-exists es-loc_wf decidable__lt bag-size_wf event-ordering+_subtype nat_wf false_wf add_functionality_wrt_le add-commutes zero-add le-add-cancel bag-member-iff-size State-comb_wf eclass_wf es-E_wf decidable__le not-le-2 less-iff-le condition-implies-le minus-add minus-one-mul add-swap add-associates add-zero le-add-cancel2 less_than_wf class-ap_wf all_wf Id_wf le_wf event-ordering+_wf bag_wf

Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].
    es-total-class(es;State-comb(init;f;X))  supposing  \mforall{}l:Id.  (1  \mleq{}  \#(init  l))



Date html generated: 2015_07_22-PM-00_20_58
Last ObjectModification: 2015_01_28-AM-10_12_42

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