Nuprl Lemma : qsum_wf
∀[a,b:ℤ]. ∀[E:{a..b-} ⟶ ℚ]. (Σa ≤ j < b. E[j] ∈ ℚ)
Proof
Definitions occuring in Statement :
qsum: Σa ≤ j < b. E[j],
rationals: ℚ,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
qsum: Σa ≤ j < b. E[j],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
crng: CRng,
so_lambda: λ2x.t[x],
so_apply: x[s],
qrng: <ℚ+*>,
rng_car: |r|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
rng_sum_wf,
qrng_wf,
crng_wf,
rationals_wf,
int_seg_wf,
rng_car_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
intEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. \mforall{}[E:\{a..b\msupminus{}\} {}\mrightarrow{} \mBbbQ{}]. (\mSigma{}a \mleq{} j < b. E[j] \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_06_16
Last ObjectModification:
2015_12_27-PM-07_45_03
Theory : rationals
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