Nuprl Lemma : vs-zero-mul
∀[K:Rng]. ∀[vs:VectorSpace(K)]. ∀[k:|K|]. (k * 0 = 0 ∈ Point(vs))
Proof
Definitions occuring in Statement :
vs-mul: a * x,
vs-0: 0,
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
true: True,
all: ∀x:A. B[x],
rng: Rng,
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
vs-0_wf,
vs-mul_wf,
vs-point_wf,
rng_wf,
vector-space_wf,
rng_car_wf,
equal_wf,
squash_wf,
true_wf,
vs-mul-linear,
rng_sig_wf,
vs-zero-add,
iff_weakening_equal,
vs-neg_wf,
vs-add_wf,
vs-add-neg,
vs-add-assoc,
vs-add-comm
Rules used in proof :
natural_numberEquality,
dependent_functionElimination,
because_Cache,
axiomEquality,
isect_memberEquality,
sqequalRule,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
applyLambdaEquality
Latex:
\mforall{}[K:Rng]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[k:|K|]. (k * 0 = 0)
Date html generated:
2018_05_22-PM-09_41_22
Last ObjectModification:
2018_01_09-PM-01_04_06
Theory : linear!algebra
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