Nuprl Lemma : vector-space_wf
∀K:RngSig. (VectorSpace(K) ∈ 𝕌')
Proof
Definitions occuring in Statement :
vector-space: VectorSpace(K),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
infix_ap: x f y,
prop: ℙ,
and: P ∧ Q,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
vs-point: Point(vs),
vector-space: VectorSpace(K),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
rng_sig_wf,
rng_plus_wf,
rng_times_wf,
infix_ap_wf,
rng_zero_wf,
rng_one_wf,
rng_car_wf,
equal_wf,
all_wf,
subtype_rel_self,
record+_wf,
top_wf,
record_wf
Rules used in proof :
rename,
setElimination,
functionExtensionality,
productEquality,
because_Cache,
functionEquality,
setEquality,
dependentIntersectionEqElimination,
hypothesisEquality,
instantiate,
applyEquality,
dependentIntersectionElimination,
tokenEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
atomEquality,
hypothesis,
cumulativity,
lambdaEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}K:RngSig. (VectorSpace(K) \mmember{} \mBbbU{}')
Date html generated:
2018_05_22-PM-09_40_11
Last ObjectModification:
2018_01_09-AM-10_14_16
Theory : linear!algebra
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