Nuprl Lemma : bm_lookup_wf

[T,Key:Type]. ∀[compare:bm_compare(Key)]. ∀[x:Key]. ∀[m:binary-map(T;Key)].
  bm_lookup(compare;m;x) ∈ supposing ↑bm_inDomain(compare;m;x)


Proof




Definitions occuring in Statement :  bm_lookup: bm_lookup(compare;m;x) bm_inDomain: bm_inDomain(compare;m;x) bm_compare: bm_compare(K) binary-map: binary-map(T;Key) assert: b uimplies: supposing a uall: [x:A]. B[x] member: t ∈ T universe: Type
Lemmas :  nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf assert_wf bm_inDomain_wf bm_cnt_prop_wf le_wf binary_map_size_wf int_seg_wf 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 binary_map-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base unit_wf2 unit_subtype_base it_wf bm_cnt_prop_E true_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom not-le-2 subtract-is-less lelt_wf bm_cnt_prop_T bm_T_wf equal-wf-base-T int_subtype_base bm_numItems_wf bm_T-wf2 member_wf decidable__lt not-equal-2 le-add-cancel-alt sq_stable__le add-mul-special zero-mul nat_wf binary_map_wf binary-map_wf bm_compare_wf valueall-type-has-valueall int-valueall-type lt_int_wf assert_of_lt_int iff_imp_equal_bool btrue_wf iff_wf evalall-reduce
\mforall{}[T,Key:Type].  \mforall{}[compare:bm\_compare(Key)].  \mforall{}[x:Key].  \mforall{}[m:binary-map(T;Key)].
    bm\_lookup(compare;m;x)  \mmember{}  T  supposing  \muparrow{}bm\_inDomain(compare;m;x)



Date html generated: 2015_07_17-AM-08_19_52
Last ObjectModification: 2015_01_27-PM-00_37_45

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