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
Home
Index