Nuprl Lemma : one-dim-vs_wf
∀[K:Rng]. (one-dim-vs(K) ∈ VectorSpace(K))
Proof
Definitions occuring in Statement :
one-dim-vs: one-dim-vs(K),
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
squash: ↓T,
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
rng: Rng,
one-dim-vs: one-dim-vs(K),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
rng_times_assoc,
rng_times_zero,
rng_times_one,
rng_times_over_plus,
rng_plus_comm,
iff_weakening_equal,
rng_plus_assoc,
true_wf,
squash_wf,
equal_wf,
rng_times_wf,
rng_plus_wf,
infix_ap_wf,
rng_zero_wf,
rng_car_wf,
mk-vs_wf
Rules used in proof :
axiomEquality,
independent_pairFormation,
independent_functionElimination,
productElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
applyEquality,
lambdaFormation,
independent_isectElimination,
hypothesisEquality,
lambdaEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:Rng]. (one-dim-vs(K) \mmember{} VectorSpace(K))
Date html generated:
2018_05_22-PM-09_41_55
Last ObjectModification:
2018_01_09-AM-10_43_54
Theory : linear!algebra
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