Nuprl Lemma : free-vs_wf
∀[S:Type]. ∀[K:CRng]. (free-vs(K;S) ∈ VectorSpace(K))
Proof
Definitions occuring in Statement :
free-vs: free-vs(K;S),
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
true: True,
prop: ℙ,
squash: ↓T,
top: Top,
cand: A c∧ B,
and: P ∧ Q,
guard: {T},
subtype_rel: A ⊆r B,
free-vs: free-vs(K;S),
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
formal-sum: formal-sum(K;S),
basic-formal-sum: basic-formal-sum(K;S),
rng: Rng,
crng: CRng,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
crng_wf,
formal-sum-mul-add,
rng_times_wf,
infix_ap_wf,
formal-sum-mul-mul,
formal-sum-mul-0,
formal-sum-mul-1,
formal-sum-mul-linear,
iff_weakening_equal,
formal-sum-add-comm,
true_wf,
squash_wf,
equal_wf,
formal-sum-add-assoc,
formal-sum-mul_wf,
formal-sum-add_wf,
rng_car_wf,
subtype_rel_transitivity,
bag_wf,
empty-bag_wf,
mk-vs_wf,
bfs-equiv-rel,
bfs-equiv_wf,
basic-formal-sum_wf,
subtype_quotient,
formal-sum_wf
Rules used in proof :
axiomEquality,
independent_functionElimination,
productElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
imageElimination,
independent_pairFormation,
voidEquality,
voidElimination,
lambdaFormation,
productEquality,
instantiate,
isectEquality,
equalitySymmetry,
equalityTransitivity,
applyEquality,
universeEquality,
isect_memberEquality,
dependent_functionElimination,
independent_isectElimination,
lambdaEquality,
because_Cache,
sqequalRule,
cumulativity,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:CRng]. (free-vs(K;S) \mmember{} VectorSpace(K))
Date html generated:
2018_05_22-PM-09_46_08
Last ObjectModification:
2018_01_09-PM-00_25_15
Theory : linear!algebra
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