### Nuprl Lemma : cycle_wf

[n:ℕ]. ∀[L:ℕList].  (cycle(L) ∈ ℕn ⟶ ℕn)

Proof

Definitions occuring in Statement :  cycle: cycle(L) list: List int_seg: {i..j-} nat: uall: [x:A]. B[x] member: t ∈ T function: x:A ⟶ B[x] natural_number: \$n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T cycle: cycle(L) nat: all: x:A. B[x] or: P ∨ Q let: let so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top so_apply: x[s1;s2;s3] ifthenelse: if then else fi  btrue: tt cons: [a b] bfalse: ff int_seg: {i..j-} prop: implies:  Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a iff: ⇐⇒ Q not: ¬A rev_implies:  Q false: False ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] subtype_rel: A ⊆B guard: {T} colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] decidable: Dec(P) nil: [] so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b squash: T less_than': less_than'(a;b)
Lemmas referenced :  int_seg_wf list-cases null_nil_lemma list_ind_nil_lemma product_subtype_list null_cons_lemma list_ind_cons_lemma reduce_hd_cons_lemma list_wf nat_wf eq_int_wf bool_wf equal-wf-T-base assert_wf equal_wf bnot_wf not_wf uiff_transitivity eqtt_to_assert assert_of_eq_int iff_transitivity iff_weakening_uiff eqff_to_assert assert_of_bnot nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int hd_wf cons_wf length_cons_ge_one subtype_rel_list top_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality hypothesis dependent_functionElimination unionElimination sqequalRule isect_memberEquality voidElimination voidEquality promote_hyp hypothesis_subsumption productElimination axiomEquality equalityTransitivity equalitySymmetry because_Cache lambdaEquality baseClosed intEquality lambdaFormation equalityElimination independent_functionElimination independent_isectElimination independent_pairFormation impliesFunctionality intWeakElimination dependent_pairFormation int_eqEquality computeAll applyEquality applyLambdaEquality dependent_set_memberEquality addEquality instantiate cumulativity imageElimination

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[L:\mBbbN{}n  List].    (cycle(L)  \mmember{}  \mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n)

Date html generated: 2017_04_17-AM-08_16_59
Last ObjectModification: 2017_02_27-PM-04_40_37

Theory : list_1

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