### Nuprl Lemma : select-tuple_wf

`∀[L:Type List]. ∀[n:ℕ]. ∀[k:ℤ].  ∀[x:tuple-type(L)]. (x.n ∈ L[n]) supposing n < ||L|| ∧ (k = ||L|| ∈ ℤ)`

Proof

Definitions occuring in Statement :  select-tuple: `x.n` tuple-type: `tuple-type(L)` select: `L[n]` length: `||as||` list: `T List` nat: `ℕ` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` and: `P ∧ Q` member: `t ∈ T` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` cons: `[a / b]` colength: `colength(L)` decidable: `Dec(P)` 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)` select-tuple: `x.n` bool: `𝔹` unit: `Unit` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` bfalse: `ff` pi1: `fst(t)` le: `A ≤ B` bnot: `¬bb` assert: `↑b` int_upper: `{i...}` cand: `A c∧ B` pi2: `snd(t)`
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 tuple-type_wf length_wf equal-wf-base-T less_than_transitivity1 less_than_irreflexivity nat_wf equal-wf-T-base colength_wf_list list_wf list-cases length_of_nil_lemma tupletype_nil_lemma stuck-spread base_wf unit_wf2 equal-wf-base int_subtype_base product_subtype_list 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 equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base decidable__equal_int length_of_cons_lemma tupletype_cons_lemma ifthenelse_wf null_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int null_nil_lemma null_cons_lemma non_neg_length eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int int_upper_subtype_nat false_wf nequal-le-implies zero-add select-cons-tl int_upper_properties decidable__lt add-is-int-iff
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry productEquality instantiate universeEquality applyEquality because_Cache unionElimination baseClosed productElimination promote_hyp hypothesis_subsumption applyLambdaEquality dependent_set_memberEquality addEquality cumulativity imageElimination equalityElimination pointwiseFunctionality baseApply closedConclusion

Latex:
\mforall{}[L:Type  List].  \mforall{}[n:\mBbbN{}].  \mforall{}[k:\mBbbZ{}].    \mforall{}[x:tuple-type(L)].  (x.n  \mmember{}  L[n])  supposing  n  <  ||L||  \mwedge{}  (k  =  ||L||)

Date html generated: 2017_04_17-AM-09_29_35
Last ObjectModification: 2017_02_27-PM-05_30_23

Theory : tuples

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