Nuprl Lemma : rsum-zero
∀[n,m:ℤ]. (Σ{r0 | n≤k≤m} = r0)
Proof
Definitions occuring in Statement :
rsum: Σ{x[k] | n≤k≤m},
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
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],
implies: P ⇒ Q,
and: P ∧ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsum_wf,
int-to-real_wf,
int_seg_wf,
rmul_wf,
rmul-zero-both,
req_functionality,
rsum-constant,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesis,
addEquality,
independent_functionElimination,
intEquality,
isect_memberEquality,
because_Cache,
productElimination,
independent_isectElimination
Latex:
\mforall{}[n,m:\mBbbZ{}]. (\mSigma{}\{r0 | n\mleq{}k\mleq{}m\} = r0)
Date html generated:
2016_05_18-AM-07_47_37
Last ObjectModification:
2015_12_28-AM-01_03_23
Theory : reals
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