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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