Nuprl Lemma : series-sum_wf
∀[x:ℕ ⟶ ℝ]. ∀[a:ℝ]. (Σn.x[n] = a ∈ ℙ)
Proof
Definitions occuring in Statement :
series-sum: Σn.x[n] = a,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
series-sum: Σn.x[n] = a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
converges-to_wf,
rsum_wf,
int_seg_subtype_nat,
false_wf,
int_seg_wf,
nat_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
addEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality
Latex:
\mforall{}[x:\mBbbN{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[a:\mBbbR{}]. (\mSigma{}n.x[n] = a \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_56_49
Last ObjectModification:
2015_12_28-AM-01_08_00
Theory : reals
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