### Nuprl Lemma : rsum_wf

`∀[n,m:ℤ]. ∀[x:{n..m + 1-} ⟶ ℝ].  (Σ{x[k] | n≤k≤m} ∈ ℝ)`

Proof

Definitions occuring in Statement :  rsum: `Σ{x[k] | n≤k≤m}` 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 :  rsum: `Σ{x[k] | n≤k≤m}` uall: `∀[x:A]. B[x]` member: `t ∈ T` has-value: `(a)↓` uimplies: `b supposing a` and: `P ∧ Q` prop: `ℙ` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k` callbyvalueall: callbyvalueall has-valueall: `has-valueall(a)` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B`
Lemmas referenced :  value-type-has-value int-value-type valueall-type-has-valueall list_wf real_wf list-valueall-type real-valueall-type map_wf and_wf le_wf less_than_wf from-upto_wf evalall-reduce valueall-type-real-list radd-list_wf-bag list-subtype-bag subtype_rel_self int_seg_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut callbyvalueReduce lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality independent_isectElimination hypothesis hypothesisEquality because_Cache setEquality addEquality natural_numberEquality lambdaEquality applyEquality productEquality lambdaFormation setElimination rename dependent_set_memberEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality

Latex:
\mforall{}[n,m:\mBbbZ{}].  \mforall{}[x:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  \mBbbR{}].    (\mSigma{}\{x[k]  |  n\mleq{}k\mleq{}m\}  \mmember{}  \mBbbR{})

Date html generated: 2016_05_18-AM-07_41_37
Last ObjectModification: 2015_12_28-AM-00_59_22

Theory : reals

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