Nuprl Lemma : rng_lsum_wf
∀[r:Rng]. ∀[A:Type]. ∀[f:A ⟶ |r|]. ∀[as:A List]. (Σ{r} x ∈ as. f[x] ∈ |r|)
Proof
Definitions occuring in Statement :
rng_lsum: Σ{r} x ∈ as. f[x],
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
so_apply: x[s],
rng: Rng,
rng_lsum: Σ{r} x ∈ as. f[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
list_wf,
map_wf,
rng_zero_wf,
rng_plus_wf,
rng_car_wf,
reduce_wf
Rules used in proof :
universeEquality,
functionEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
cumulativity,
because_Cache,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} |r|]. \mforall{}[as:A List]. (\mSigma{}\{r\} x \mmember{} as. f[x] \mmember{} |r|)
Date html generated:
2018_05_21-PM-09_32_38
Last ObjectModification:
2017_12_11-PM-00_35_04
Theory : matrices
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