### Nuprl Lemma : rpolynomial_wf

`∀[n:ℕ]. ∀[a:ℕn + 1 ⟶ ℝ]. ∀[x:ℝ].  ((Σi≤n. a_i * x^i) ∈ ℝ)`

Proof

Definitions occuring in Statement :  rpolynomial: `(Σi≤n. a_i * x^i)` 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 :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rpolynomial: `(Σi≤n. a_i * x^i)` nat: `ℕ` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  rsum_wf rmul_wf rnexp_wf int_seg_subtype_nat false_wf int_seg_wf real_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality lambdaEquality applyEquality addEquality independent_isectElimination independent_pairFormation lambdaFormation hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[a:\mBbbN{}n  +  1  {}\mrightarrow{}  \mBbbR{}].  \mforall{}[x:\mBbbR{}].    ((\mSigma{}i\mleq{}n.  a\_i  *  x\^{}i)  \mmember{}  \mBbbR{})

Date html generated: 2016_05_18-AM-07_44_08
Last ObjectModification: 2015_12_28-AM-01_00_19

Theory : reals

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