Nuprl Lemma : series-sum-unique
∀[x:ℕ ⟶ ℝ]. ∀[a,b:ℝ]. (a = b) supposing (Σn.x[n] = b and Σn.x[n] = a)
Proof
Definitions occuring in Statement :
series-sum: Σn.x[n] = a,
req: x = y,
real: ℝ,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
series-sum: Σn.x[n] = a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
subtype_rel: A ⊆r B,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
unique-limit,
rsum_wf,
nat_wf,
int_seg_wf,
req_inversion,
req_witness,
converges-to_wf,
int_seg_subtype_nat,
false_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
functionExtensionality,
because_Cache,
addEquality,
independent_isectElimination,
independent_functionElimination,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[x:\mBbbN{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[a,b:\mBbbR{}]. (a = b) supposing (\mSigma{}n.x[n] = b and \mSigma{}n.x[n] = a)
Date html generated:
2016_10_26-AM-09_19_38
Last ObjectModification:
2016_08_26-PM-01_40_07
Theory : reals
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