### Nuprl Lemma : poly-nth-deriv_wf

`∀[n,d:ℕ]. ∀[a:ℕn + d ⟶ ℝ].  (poly-nth-deriv(n;a) ∈ ℕd ⟶ ℝ)`

Proof

Definitions occuring in Statement :  poly-nth-deriv: `poly-nth-deriv(n;a)` real: `ℝ` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n`
Definitions unfolded in proof :  poly-nth-deriv: `poly-nth-deriv(n;a)` 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` sq_type: `SQType(T)` guard: `{T}` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` subtype_rel: `A ⊆r B` bfalse: `ff` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` subtract: `n - m`
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 real_wf nat_wf primrec0_lemma subtype_base_sq int_subtype_base zero-add 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 less_than_transitivity1 le_weakening less_than_irreflexivity eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int poly-deriv_wf itermAdd_wf int_term_value_add_lemma le_wf add-commutes add-associates add-swap
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 axiomEquality equalityTransitivity equalitySymmetry functionEquality addEquality instantiate cumulativity because_Cache unionElimination equalityElimination productElimination applyEquality promote_hyp dependent_set_memberEquality

Latex:
\mforall{}[n,d:\mBbbN{}].  \mforall{}[a:\mBbbN{}n  +  d  {}\mrightarrow{}  \mBbbR{}].    (poly-nth-deriv(n;a)  \mmember{}  \mBbbN{}d  {}\mrightarrow{}  \mBbbR{})

Date html generated: 2017_10_03-PM-00_14_05
Last ObjectModification: 2017_07_28-AM-08_36_51

Theory : reals

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