### Nuprl Lemma : member-nth-tl-implies-member

`∀[T:Type]. ∀x:T. ∀n:ℕ. ∀L:T List.  ((x ∈ nth_tl(n;L)) `` (x ∈ L))`

Proof

Definitions occuring in Statement :  l_member: `(x ∈ l)` nth_tl: `nth_tl(n;as)` list: `T List` nat: `ℕ` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` nth_tl: `nth_tl(n;as)` le_int: `i ≤z j` lt_int: `i <z j` bnot: `¬bb` ifthenelse: `if b then t else f fi ` bfalse: `ff` subtract: `n - m` btrue: `tt` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` nat: `ℕ` or: `P ∨ Q` uimplies: `b supposing a` sq_type: `SQType(T)` guard: `{T}` uiff: `uiff(P;Q)` and: `P ∧ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` cons: `[a / b]` top: `Top`
Lemmas referenced :  l_member_wf list_wf ifthenelse_wf le_int_wf nth_tl_wf tl_wf subtract_wf all_wf set_wf less_than_wf primrec-wf2 nat_wf assert_wf bnot_wf not_wf le_wf bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert assert_of_le_int eqff_to_assert iff_transitivity iff_weakening_uiff assert_of_bnot list-cases reduce_tl_nil_lemma nth_tl_nil product_subtype_list reduce_tl_cons_lemma cons_member equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin sqequalRule hypothesis lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality rename setElimination natural_numberEquality because_Cache lambdaEquality functionEquality intEquality introduction universeEquality equalityTransitivity equalitySymmetry dependent_functionElimination unionElimination instantiate cumulativity independent_isectElimination independent_functionElimination productElimination independent_pairFormation impliesFunctionality promote_hyp hypothesis_subsumption isect_memberEquality voidElimination voidEquality inrFormation

Latex:
\mforall{}[T:Type].  \mforall{}x:T.  \mforall{}n:\mBbbN{}.  \mforall{}L:T  List.    ((x  \mmember{}  nth\_tl(n;L))  {}\mRightarrow{}  (x  \mmember{}  L))

Date html generated: 2016_05_14-PM-01_27_21
Last ObjectModification: 2015_12_26-PM-04_51_02

Theory : list_1

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