Nuprl Lemma : real-vec-sum-shift
∀[k,n,m:ℤ]. ∀[x:Top]. (Σ{x[i] | n≤i≤m} ~ Σ{x[i + k] | n - k≤i≤m - k})
Proof
Definitions occuring in Statement :
real-vec-sum: Σ{x[k] | n≤k≤m},
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
subtract: n - m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-sum: Σ{x[k] | n≤k≤m},
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
rsum-shift,
istype-void,
istype-top,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality_alt,
voidElimination,
hypothesis,
axiomSqEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[k,n,m:\mBbbZ{}]. \mforall{}[x:Top]. (\mSigma{}\{x[i] | n\mleq{}i\mleq{}m\} \msim{} \mSigma{}\{x[i + k] | n - k\mleq{}i\mleq{}m - k\})
Date html generated:
2019_10_30-AM-08_02_46
Last ObjectModification:
2019_09_18-PM-02_41_04
Theory : reals
Home
Index