Nuprl Lemma : es-prior-interface-val-pred

∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
  prior(X)(e) = if pred(e) ∈b X then pred(e) else prior(X)(pred(e)) fi  ∈ E supposing ↑e ∈b prior(X)


Proof




Definitions occuring in Statement :  es-prior-interface: prior(X),  eclass-val: X(e),  in-eclass: e ∈b X,  eclass: EClass(A[eo; e]),  event-ordering+: EO+(Info),  es-pred: pred(e),  es-E: E,  assert: ↑b,  ifthenelse: if b then t else f fi ,  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  top: Top,  universe: Type,  equal: s = t ∈ T
Lemmas :  assert_wf,  in-eclass_wf,  es-prior-interface_wf0,  es-interface-subtype_rel2,  es-E_wf,  event-ordering+_subtype,  event-ordering+_wf,  top_wf,  subtype_top,  eclass_wf,  es-is-prior-interface-pred,  es-pred_wf,  bool_wf,  equal-wf-T-base,  bnot_wf,  not_wf,  eqtt_to_assert,  uiff_transitivity,  eqff_to_assert,  assert_of_bnot,  es-prior-interface-val,  es-locl-iff,  eclass-val_wf2,  es-prior-interface_wf,  es-E-interface_wf,  es-pred-locl,  decidable__es-locl,  assert_elim,  and_wf,  equal_wf,  not_assert_elim,  btrue_neq_bfalse,  es-locl_transitivity2,  es-le_weakening,  es-locl-total,  es-loc-pred

Latex:
\mforall{}[Info:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[X:EClass(Top)].  \mforall{}[e:E].
    prior(X)(e)  =  if  pred(e)  \mmember{}\msubb{}  X  then  pred(e)  else  prior(X)(pred(e))  fi    supposing  \muparrow{}e  \mmember{}\msubb{}  prior(X)



Date html generated: 2015_07_21-PM-02_47_11
Last ObjectModification: 2015_01_27-PM-07_39_04

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