### Nuprl Lemma : rsum'_wf

`∀[n,m:ℤ]. ∀[x:{n..m + 1-} ⟶ ℝ].  (rsum'(n;m;k.x[k]) ∈ ℝ)`

Proof

Definitions occuring in Statement :  rsum': `rsum'(n;m;k.x[k])` real: `ℝ` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` real: `ℝ` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q`
Lemmas referenced :  int_seg_wf real_wf rsum'-eq-rsum regular-int-seq_wf nat_plus_wf real-regular rsum_wf less_than_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry functionEquality extract_by_obid isectElimination thin hypothesisEquality addEquality natural_numberEquality isect_memberEquality because_Cache intEquality dependent_set_memberEquality functionExtensionality applyEquality lambdaEquality independent_pairFormation imageMemberEquality baseClosed hyp_replacement applyLambdaEquality

Latex:
\mforall{}[n,m:\mBbbZ{}].  \mforall{}[x:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  \mBbbR{}].    (rsum'(n;m;k.x[k])  \mmember{}  \mBbbR{})

Date html generated: 2017_10_03-AM-08_57_17
Last ObjectModification: 2017_09_20-PM-06_01_53

Theory : reals

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