Nuprl Lemma : real-vec-sum_wf
∀[n,m:ℤ]. ∀[k:ℕ]. ∀[x:{n..m + 1-} ⟶ ℝ^k]. (Σ{x[k] | n≤k≤m} ∈ ℝ^k)
Proof
Definitions occuring in Statement :
real-vec-sum: Σ{x[k] | n≤k≤m},
real-vec: ℝ^n,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-sum: Σ{x[k] | n≤k≤m},
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ
Lemmas referenced :
rsum_wf,
int_seg_wf,
real_wf,
istype-nat,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
universeIsType,
addEquality,
natural_numberEquality,
hypothesis,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[k:\mBbbN{}]. \mforall{}[x:\{n..m + 1\msupminus{}\} {}\mrightarrow{} \mBbbR{}\^{}k]. (\mSigma{}\{x[k] | n\mleq{}k\mleq{}m\} \mmember{} \mBbbR{}\^{}k)
Date html generated:
2019_10_30-AM-08_00_38
Last ObjectModification:
2019_09_17-PM-02_26_45
Theory : reals
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