### Nuprl Lemma : select-repn

`∀[x:Top]. ∀[n:ℕ]. ∀[i:ℕn].  (repn(n;x)[i] ~ x)`

Proof

Definitions occuring in Statement :  repn: `repn(n;x)` select: `L[n]` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  repn: `repn(n;x)` uall: `∀[x:A]. B[x]` member: `t ∈ T` 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` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ 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 int_seg_wf primrec0_lemma stuck-spread base_wf int_seg_properties decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma primrec-unroll eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int intformeq_wf int_formula_prop_eq_lemma eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int select-cons le_int_wf assert_of_le_int le_wf nat_wf top_wf decidable__lt lelt_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep 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 independent_pairFormation computeAll independent_functionElimination sqequalAxiom baseClosed because_Cache productElimination unionElimination equalityElimination equalityTransitivity equalitySymmetry promote_hyp instantiate cumulativity dependent_set_memberEquality

Latex:
\mforall{}[x:Top].  \mforall{}[n:\mBbbN{}].  \mforall{}[i:\mBbbN{}n].    (repn(n;x)[i]  \msim{}  x)

Date html generated: 2017_04_17-AM-07_50_00
Last ObjectModification: 2017_02_27-PM-04_23_56

Theory : list_1

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