Nuprl Lemma : vs-exp_wf
∀[K:Rng]. ∀[S:Type]. ∀[V:VectorSpace(K)]. (V^S ∈ VectorSpace(K))
Proof
Definitions occuring in Statement :
vs-exp: V^S,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng: Rng
Definitions unfolded in proof :
rng: Rng,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
vs-exp: V^S,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
vector-space_wf,
vs-sum_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
rename,
setElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
lambdaEquality,
cumulativity,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:Rng]. \mforall{}[S:Type]. \mforall{}[V:VectorSpace(K)]. (V\^{}S \mmember{} VectorSpace(K))
Date html generated:
2018_05_22-PM-09_42_36
Last ObjectModification:
2018_01_09-PM-01_03_12
Theory : linear!algebra
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