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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