Nuprl Lemma : vs-lin-indep_wf
∀[K:Rng]. ∀[vs:VectorSpace(K)]. ∀[P:Point(vs) ⟶ ℙ]. (vs-lin-indep(K;vs;v.P[v]) ∈ ℙ)
Proof
Definitions occuring in Statement :
vs-lin-indep: vs-lin-indep(K;vs;v.P[v]),
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
rng: Rng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vs-lin-indep: vs-lin-indep(K;vs;v.P[v]),
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
rng: Rng,
so_apply: x[s],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x]
Lemmas referenced :
nat_wf,
int_seg_wf,
vs-point_wf,
subtype_rel_self,
inject_wf,
rng_car_wf,
equal_wf,
sum-in-vs_wf,
vs-mul_wf,
vs-0_wf,
rng_zero_wf,
vector-space_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
setEquality,
because_Cache,
applyEquality,
instantiate,
universeEquality,
functionExtensionality,
lambdaEquality_alt,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
universeIsType,
axiomEquality,
functionIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
dependent_functionElimination
Latex:
\mforall{}[K:Rng]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[P:Point(vs) {}\mrightarrow{} \mBbbP{}]. (vs-lin-indep(K;vs;v.P[v]) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_26_37
Last ObjectModification:
2019_08_14-PM-06_35_20
Theory : linear!algebra
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