Nuprl Lemma : until-class-simple-comb

∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(Top)].
  ((X until Y) = λxs,ys.if bag-null(ys) then xs else {} fi |X;Prior(Y)| ∈ EClass(A))


Proof




Definitions occuring in Statement :  simple-comb2: λx,y.F[x; y]|X;Y|,  primed-class: Prior(X),  until-class: (X until Y),  eclass: EClass(A[eo; e]),  ifthenelse: if b then t else f fi ,  uall: ∀[x:A]. B[x],  top: Top,  universe: Type,  equal: s = t ∈ T,  bag-null: bag-null(bs),  empty-bag: {}
Lemmas :  class-pred-cases,  uiff_transitivity,  equal-wf-T-base,  assert_wf,  bag_wf,  eqtt_to_assert,  assert-bag-null,  no-classrel-iff-empty,  primed-class_wf,  iff_transitivity,  bnot_wf,  not_wf,  iff_weakening_uiff,  eqff_to_assert,  assert_of_bnot,  equal_wf,  bool_wf,  bool_cases_sqequal,  subtype_base_sq,  bool_subtype_base,  assert-bnot,  empty-bag_wf,  all_wf,  classrel_wf,  es-E_wf,  event-ordering+_subtype,  event-ordering+_wf,  top_wf,  primed-classrel,  es-locl_wf,  alle-lt_wf,  Id_wf,  es-loc_wf,  es-le_wf

Latex:
\mforall{}[Info,A:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(Top)].
    ((X  until  Y)  =  \mlambda{}xs,ys.if  bag-null(ys)  then  xs  else  \{\}  fi  |X;Prior(Y)|)



Date html generated: 2015_07_21-PM-03_19_24
Last ObjectModification: 2015_01_27-PM-07_22_48

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