Nuprl Lemma : loop-class-program_wf

[Info,B:Type].
  ∀[X:EClass(B ─→ bag(B))]. ∀[init:Id ─→ bag(B)]. ∀[pr:LocalClass(X)].
    (loop-class-program(init;pr) ∈ LocalClass(loop-class(X;init))) 
  supposing valueall-type(B)


Proof




Definitions occuring in Statement :  loop-class-program: loop-class-program(init;pr) loop-class: loop-class(X;init) local-class: LocalClass(X) eclass: EClass(A[eo; e]) Id: Id valueall-type: valueall-type(T) uimplies: supposing a uall: [x:A]. B[x] member: t ∈ T function: x:A ─→ B[x] universe: Type bag: bag(T)
Lemmas :  loop-class_wf hdf-buffer_wf Id_wf es-E_wf event-ordering+_subtype event-ordering+_wf all_wf equal_wf bag_wf class-ap_wf hdf-ap_wf iterate-hdataflow_wf es-loc_wf map_wf es-info_wf es-before_wf hdataflow_wf local-class_wf eclass_wf valueall-type_wf es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_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 primed-class-opt-cases es-interface-subtype_rel2 top_wf es-first_wf2 bool_wf eqtt_to_assert map_nil_lemma iter_hdf_nil_lemma simple-hdf-buffer_wf uiff_transitivity equal-wf-T-base assert_wf bnot_wf not_wf eqff_to_assert assert_of_bnot decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul es-pred_wf subtype_rel_list map_cons_lemma iter_hdf_cons_lemma es-pred-locl es-causl_weakening primed-class-opt_wf map_append_sq iterate-hdf-append squash_wf true_wf list_wf es-loc-pred iff_weakening_equal lt_int_wf bag-size_wf assert_of_lt_int bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot atom2_subtype_base es-pred-loc-base hdataflow-ext unit_wf2 valueall-type-has-valueall bag-valueall-type bag-combine_wf evalall-reduce hdf-run_wf assert-bag-null bag-null_wf bag_size_empty_lemma bag-size-zero empty-bag_wf iterate-hdf-buffer-simple bag_combine_empty_lemma

Latex:
\mforall{}[Info,B:Type].
    \mforall{}[X:EClass(B  {}\mrightarrow{}  bag(B))].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[pr:LocalClass(X)].
        (loop-class-program(init;pr)  \mmember{}  LocalClass(loop-class(X;init))) 
    supposing  valueall-type(B)



Date html generated: 2015_07_22-PM-00_02_27
Last ObjectModification: 2015_02_04-PM-05_12_20

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