Nuprl Lemma : lsum_wf
∀[T:Type]. ∀[L:T List]. ∀[f:{x:T| (x ∈ L)} ⟶ ℤ]. (Σ(f[x] | x ∈ L) ∈ ℤ)
Proof
Definitions occuring in Statement :
lsum: Σ(f[x] | x ∈ L),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
lsum: Σ(f[x] | x ∈ L),
member: t ∈ T,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
list-subtype,
l_sum_wf,
map_wf,
l_member_wf,
istype-int,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
intEquality,
lambdaEquality_alt,
applyEquality,
setIsType,
universeIsType,
functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:\{x:T| (x \mmember{} L)\} {}\mrightarrow{} \mBbbZ{}]. (\mSigma{}(f[x] | x \mmember{} L) \mmember{} \mBbbZ{})
Date html generated:
2020_05_19-PM-09_46_35
Last ObjectModification:
2019_11_12-PM-11_12_32
Theory : list_1
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