Nuprl Lemma : member-loop-class-memory

∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  (e ∈b loop-class-memory(X;init) ~ 0 <z #(init loc(e)))


Proof




Definitions occuring in Statement :  loop-class-memory: loop-class-memory(X;init),  member-eclass: e ∈b X,  eclass: EClass(A[eo; e]),  event-ordering+: EO+(Info),  es-loc: loc(e),  es-E: E,  Id: Id,  lt_int: i <z j,  uall: ∀[x:A]. B[x],  apply: f a,  function: x:A ⟶ B[x],  natural_number: $n,  universe: Type,  sqequal: s ~ t,  bag-size: #(bs),  bag: bag(T)
Definitions unfolded in proof :  all: ∀x:A. B[x],  member: t ∈ T,  uall: ∀[x:A]. B[x],  or: P ∨ Q,  uiff: uiff(P;Q),  and: P ∧ Q,  uimplies: b supposing a,  subtype_rel: A ⊆r B,  nat: ℕ,  assert: ↑b,  ifthenelse: if b then t else f fi ,  btrue: tt,  bfalse: ff,  iff: P ⇐⇒ Q,  implies: P ⇒ Q,  false: False,  not: ¬A,  rev_uimplies: rev_uimplies(P;Q),  prop: ℙ,  rev_implies: P ⇐ Q,  true: True,  sq_type: SQType(T),  guard: {T},  so_lambda: λ2x y.t[x; y],  so_apply: x[s1;s2]

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



Date html generated: 2016_05_17-AM-11_15_29
Last ObjectModification: 2015_12_29-PM-05_13_42

Theory : process-model


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