Nuprl Lemma : real-vec-sum-empty
∀[n,m:ℤ]. ∀[x:Top]. Σ{x[k] | n≤k≤m} ~ λi.r0 supposing m < n
Proof
Definitions occuring in Statement :
real-vec-sum: Σ{x[k] | n≤k≤m},
int-to-real: r(n),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
lambda: λx.A[x],
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
real-vec-sum: Σ{x[k] | n≤k≤m},
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
rsum-empty,
istype-void,
istype-less_than,
istype-top,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
isect_memberEquality_alt,
voidElimination,
hypothesis,
independent_isectElimination,
axiomSqEquality,
hypothesisEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[x:Top]. \mSigma{}\{x[k] | n\mleq{}k\mleq{}m\} \msim{} \mlambda{}i.r0 supposing m < n
Date html generated:
2019_10_30-AM-08_01_55
Last ObjectModification:
2019_09_17-PM-05_17_33
Theory : reals
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