### Nuprl Lemma : orbit_wf

`∀[T:Type]. ∀[f:T ⟶ T]. ∀[L:T List].  (orbit(T;f;L) ∈ ℙ)`

Proof

Definitions occuring in Statement :  orbit: `orbit(T;f;L)` list: `T List` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` orbit: `orbit(T;f;L)` prop: `ℙ` and: `P ∧ Q` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` less_than: `a < b` squash: `↓T` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` le: `A ≤ B` less_than': `less_than'(a;b)` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` so_apply: `x[s]`
Lemmas referenced :  less_than_wf length_wf no_repeats_wf all_wf int_seg_wf equal_wf select_wf int_seg_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma eq_int_wf subtract_wf bool_wf eqtt_to_assert assert_of_eq_int false_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int itermAdd_wf int_term_value_add_lemma intformeq_wf itermSubtract_wf int_formula_prop_eq_lemma int_term_value_subtract_lemma list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule productEquality extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality cumulativity hypothesisEquality hypothesis because_Cache lambdaEquality applyEquality functionExtensionality setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination lambdaFormation equalityElimination equalityTransitivity equalitySymmetry promote_hyp instantiate independent_functionElimination addEquality axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  T].  \mforall{}[L:T  List].    (orbit(T;f;L)  \mmember{}  \mBbbP{})

Date html generated: 2017_04_17-AM-08_14_03
Last ObjectModification: 2017_02_27-PM-04_39_21

Theory : list_1

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