### Nuprl Lemma : rsum'-rsum

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

Proof

Definitions occuring in Statement :  rsum: `Σ{x[k] | n≤k≤m}` rsum': `rsum'(n;m;k.x[k])` req: `x = y` real: `ℝ` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` so_apply: `x[s]` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` stable: `Stable{P}` uimplies: `b supposing a` not: `¬A` prop: `ℙ` or: `P ∨ Q` implies: `P `` Q` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` false: `False` label: `...\$L... t` real: `ℝ` nat_plus: `ℕ+` all: `∀x:A. B[x]` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]`

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

Date html generated: 2020_05_20-AM-11_10_23
Last ObjectModification: 2020_01_03-AM-11_17_46

Theory : reals

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