Nuprl Lemma : select-nth_tl

[n,x:ℕ]. ∀[L:Top List].  (nth_tl(n;L)[x] L[n x])


Proof




Definitions occuring in Statement :  select: L[n] nth_tl: nth_tl(n;as) list: List nat: uall: [x:A]. B[x] top: Top add: m sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A all: x:A. B[x] top: Top and: P ∧ Q prop: nth_tl: nth_tl(n;as) le_int: i ≤j lt_int: i <j bnot: ¬bb ifthenelse: if then else fi  bfalse: ff subtract: m btrue: tt decidable: Dec(P) or: P ∨ Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) sq_type: SQType(T) guard: {T} assert: b select: L[n] nil: [] so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] cons: [a b]
Lemmas referenced :  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 list_wf top_wf nat_wf zero-add decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf tl_wf list-cases reduce_tl_nil_lemma stuck-spread base_wf product_subtype_list reduce_tl_cons_lemma select-cons-tl decidable__lt itermAdd_wf int_term_value_add_lemma general_arith_equation1
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom because_Cache unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination promote_hyp instantiate cumulativity baseClosed hypothesis_subsumption addEquality

Latex:
\mforall{}[n,x:\mBbbN{}].  \mforall{}[L:Top  List].    (nth\_tl(n;L)[x]  \msim{}  L[n  +  x])



Date html generated: 2017_04_17-AM-07_49_32
Last ObjectModification: 2017_02_27-PM-04_23_49

Theory : list_1


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