### Nuprl Lemma : series-sum_wf

`∀[x:ℕ ⟶ ℝ]. ∀[a:ℝ].  (Σn.x[n] = a ∈ ℙ)`

Proof

Definitions occuring in Statement :  series-sum: `Σn.x[n] = a` real: `ℝ` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  series-sum: `Σn.x[n] = a` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` nat: `ℕ` so_apply: `x[s]` 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`
Lemmas referenced :  converges-to_wf rsum_wf int_seg_subtype_nat false_wf int_seg_wf nat_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin lambdaEquality natural_numberEquality setElimination rename hypothesisEquality applyEquality addEquality independent_isectElimination independent_pairFormation lambdaFormation hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality

Latex:
\mforall{}[x:\mBbbN{}  {}\mrightarrow{}  \mBbbR{}].  \mforall{}[a:\mBbbR{}].    (\mSigma{}n.x[n]  =  a  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-07_56_49
Last ObjectModification: 2015_12_28-AM-01_08_00

Theory : reals

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