### Nuprl Lemma : poly-deriv_wf

`∀n:ℕ. ∀a:ℕn + 1 ⟶ ℝ.  (poly-deriv(a) ∈ ℕn ⟶ ℝ)`

Proof

Definitions occuring in Statement :  poly-deriv: `poly-deriv(a)` real: `ℝ` int_seg: `{i..j-}` nat: `ℕ` all: `∀x:A. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n`
Definitions unfolded in proof :  less_than: `a < b` le: `A ≤ B` prop: `ℙ` subtract: `n - m` top: `Top` not: `¬A` implies: `P `` Q` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` or: `P ∨ Q` decidable: `Dec(P)` ge: `i ≥ j ` lelt: `i ≤ j < k` uimplies: `b supposing a` and: `P ∧ Q` uiff: `uiff(P;Q)` nat: `ℕ` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` poly-deriv: `poly-deriv(a)` member: `t ∈ T` all: `∀x:A. B[x]`
Lemmas referenced :  rmul_wf int-to-real_wf add-member-int_seg2 nat_properties decidable__le subtract_wf satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermSubtract_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf add-subtract-cancel decidable__lt intformless_wf int_formula_prop_less_lemma lelt_wf int_seg_wf real_wf nat_wf
Rules used in proof :  functionEquality computeAll voidEquality voidElimination isect_memberEquality intEquality int_eqEquality dependent_pairFormation unionElimination dependent_functionElimination independent_pairFormation dependent_set_memberEquality independent_isectElimination productElimination because_Cache applyEquality natural_numberEquality hypothesis hypothesisEquality rename setElimination addEquality thin isectElimination sqequalHypSubstitution lemma_by_obid lambdaEquality sqequalRule cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}n:\mBbbN{}.  \mforall{}a:\mBbbN{}n  +  1  {}\mrightarrow{}  \mBbbR{}.    (poly-deriv(a)  \mmember{}  \mBbbN{}n  {}\mrightarrow{}  \mBbbR{})

Date html generated: 2016_05_18-AM-10_08_05
Last ObjectModification: 2016_01_17-AM-00_37_44

Theory : reals

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