Nuprl Lemma : primed-class-cases

[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
  (Prior(X) es if first(e) then {}
  if 0 <#(X es pred(e)) then es pred(e)
  else Prior(X) es pred(e)
  fi )


Proof




Definitions occuring in Statement :  primed-class: Prior(X) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-first: first(e) es-pred: pred(e) es-E: E ifthenelse: if then else fi  lt_int: i <j uall: [x:A]. B[x] top: Top apply: a natural_number: $n universe: Type sqequal: t bag-size: #(bs) empty-bag: {}
Lemmas :  es-causl-swellfnd event-ordering+_subtype nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf es-E_wf int_seg_wf int_seg_subtype-nat decidable__le subtract_wf false_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel decidable__equal_int subtype_rel-int_seg le_weakening int_seg_properties le_wf nat_wf zero-le-nat lelt_wf es-causl_wf es-first_wf2 bool_wf eqtt_to_assert eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot lt_int_wf bag-size_wf top_wf es-pred_wf assert_of_lt_int decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul eclass_wf event-ordering+_wf

Latex:
\mforall{}[Info:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[X:EClass(Top)].  \mforall{}[e:E].
    (Prior(X)  es  e  \msim{}  if  first(e)  then  \{\}
    if  0  <z  \#(X  es  pred(e))  then  X  es  pred(e)
    else  Prior(X)  es  pred(e)
    fi  )



Date html generated: 2015_07_21-PM-03_18_30
Last ObjectModification: 2015_01_27-PM-07_19_45

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