Nuprl Lemma : series-converges-rmul-ext
∀c:ℝ. ∀x:ℕ ⟶ ℝ. (Σn.x[n]↓ ⇒ Σn.x[n] * c↓)
Proof
Definitions occuring in Statement :
series-converges: Σn.x[n]↓,
rmul: a * b,
real: ℝ,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
integer-bound,
series-sum-linear3,
series-converges-rmul,
rabs: |x|,
member: t ∈ T
Lemmas referenced :
series-converges-rmul,
integer-bound,
series-sum-linear3
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}c:\mBbbR{}. \mforall{}x:\mBbbN{} {}\mrightarrow{} \mBbbR{}. (\mSigma{}n.x[n]\mdownarrow{} {}\mRightarrow{} \mSigma{}n.x[n] * c\mdownarrow{})
Date html generated:
2018_05_22-PM-02_02_19
Last ObjectModification:
2018_05_21-AM-00_15_29
Theory : reals
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