Nuprl Lemma : power-sum_wf
∀[n:ℕ]. ∀[x:ℤ]. ∀[a:ℕn ⟶ ℤ]. (Σi<n.a[i]*x^i ∈ ℤ)
Proof
Definitions occuring in Statement :
power-sum: Σi<n.a[i]*x^i,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
power-sum: Σi<n.a[i]*x^i,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
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
Lemmas referenced :
sum_wf,
exp_wf2,
int_seg_subtype_nat,
false_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
multiplyEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbZ{}]. \mforall{}[a:\mBbbN{}n {}\mrightarrow{} \mBbbZ{}]. (\mSigma{}i<n.a[i]*x\^{}i \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-06_27_08
Last ObjectModification:
2015_12_27-PM-00_01_28
Theory : general
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