Nuprl Lemma : archive-condition-one-one

[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ─→ V]. ∀[L:consensus-rcv(V;A) List]. ∀[n1,n2:ℤ]. ∀[v1,v2:V].
  ({(n1 n2 ∈ ℤ) ∧ (v1 v2 ∈ V)}) supposing 
     (archive-condition(V;A;t;f;n2;v2;L) and 
     archive-condition(V;A;t;f;n1;v1;L))


Proof




Definitions occuring in Statement :  archive-condition: archive-condition(V;A;t;f;n;v;L) consensus-rcv: consensus-rcv(V;A) Id: Id list: List nat_plus: + uimplies: supposing a uall: [x:A]. B[x] guard: {T} and: P ∧ Q function: x:A ─→ B[x] int: universe: Type equal: t ∈ T
Lemmas :  id-deq_wf subtype_rel-deq Id_wf l_member_wf sq_stable__l_member decidable__equal_Id equal_wf set_wf length_wf_nat nat_wf archive-condition_wf general-append-cancellation cons_wf nil_wf length-singleton length_wf length_of_cons_lemma length_of_nil_lemma hd_wf listp_properties assert_of_lt_int consensus-rcv_wf list-cases cons_neq_nil product_subtype_list decidable__lt false_wf condition-implies-le minus-add minus-one-mul zero-add add-commutes add_functionality_wrt_le add-associates add-zero le-add-cancel assert_wf lt_int_wf reduce_hd_cons_lemma tl_wf reduce_tl_cons_lemma or_wf equal-wf-T-base cs-initial-rcv_wf equal-wf-base int_subtype_base le_wf exists_wf cs-rcv-vote_wf less_than_wf values-for-distinct_wf votes-from-inning_wf subtract_wf null_wf3 filter_wf5 rcvd-inning-gt_wf subtype_rel_list top_wf le_weakening2 nat_plus_subtype_nat list_wf nat_plus_wf filter_nil_lemma list_ind_nil_lemma null_nil_lemma true_wf bfalse_wf and_wf isl_wf btrue_wf btrue_neq_bfalse outl_wf not_wf null_cons_lemma length-map filter_cons_lemma map_nil_lemma remove_repeats_nil_lemma remove-repeats_wf map_wf rcvd-inning-eq_wf bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert map_cons_lemma remove_repeats_cons_lemma eqff_to_assert assert_of_bnot append_wf vote-crosses-threshold squash_wf deq_wf iff_weakening_equal consensus-rcv-crosses-threshold list_ind_cons_lemma set_subtype_base decidable__equal_int not-equal-2 le_antisymmetry_iff minus-minus add-swap le-add-cancel-alt
\mforall{}[V:Type].  \mforall{}[A:Id  List].  \mforall{}[t:\mBbbN{}\msupplus{}].  \mforall{}[f:(V  List)  {}\mrightarrow{}  V].  \mforall{}[L:consensus-rcv(V;A)  List].  \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
    (\{(n1  =  n2)  \mwedge{}  (v1  =  v2)\})  supposing 
          (archive-condition(V;A;t;f;n2;v2;L)  and 
          archive-condition(V;A;t;f;n1;v1;L))



Date html generated: 2015_07_17-AM-11_49_50
Last ObjectModification: 2015_02_04-PM-05_47_46

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