Nuprl Lemma : loop-class-memory-size-prior

[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  uiff(0 < #(init loc(e));0 < #(Prior(loop-class-memory(X;init))?init(e)))


Proof




Definitions occuring in Statement :  loop-class-memory: loop-class-memory(X;init) primed-class-opt: Prior(X)?b class-ap: X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id less_than: a < b uiff: uiff(P;Q) uall: [x:A]. B[x] apply: a function: x:A ─→ B[x] natural_number: $n universe: Type bag-size: #(bs) bag: bag(T)
Lemmas :  less_than_wf bag-size_wf es-loc_wf event-ordering+_subtype nat_wf class-ap_wf primed-class-opt_wf loop-class-memory_wf member-less_than es-E_wf event-ordering+_wf Id_wf bag_wf eclass_wf loop-class-memory-exists-prior bag-member-iff-size

Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    uiff(0  <  \#(init  loc(e));0  <  \#(Prior(loop-class-memory(X;init))?init(e)))



Date html generated: 2015_07_21-PM-02_35_39
Last ObjectModification: 2015_01_27-PM-09_44_32

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