Nuprl Lemma : relative-free-vs_wf
∀[K:CRng]. ∀[S,T:Type]. relative-free-vs(K;S;T) ∈ VectorSpace(K) supposing strong-subtype(T;S)
Proof
Definitions occuring in Statement :
relative-free-vs: relative-free-vs(K;S;T),
vector-space: VectorSpace(K),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
relative-free-vs: relative-free-vs(K;S;T),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
vs-point: Point(vs),
record-select: r.x,
free-vs: free-vs(K;S),
mk-vs: mk-vs,
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
formal-sum: formal-sum(K;S),
quotient: x,y:A//B[x; y],
crng: CRng,
rng: Rng,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
vs-quotient_wf,
free-vs_wf,
fs-in-subtype_wf,
subtype_rel_self,
formal-sum_wf,
vs-point_wf,
fs-in-subtype-subspace,
strong-subtype_wf,
istype-universe,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality_alt,
independent_isectElimination,
applyEquality,
setElimination,
rename,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[K:CRng]. \mforall{}[S,T:Type]. relative-free-vs(K;S;T) \mmember{} VectorSpace(K) supposing strong-subtype(T;S)
Date html generated:
2019_10_31-AM-06_30_28
Last ObjectModification:
2019_08_20-AM-10_33_44
Theory : linear!algebra
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