Nuprl Lemma : rv-mul-0
∀[rv:RealVectorSpace]. ∀[a:ℝ]. a*0 ≡ 0
Proof
Definitions occuring in Statement :
rv-mul: a*x,
rv-0: 0,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
ss-eq: x ≡ y,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rmul-zero-both,
rv-mul-mul,
ss-eq_weakening,
rmul_wf,
ss-eq_inversion,
req_weakening,
rv-mul_functionality,
ss-eq_functionality,
int-to-real_wf,
real-vector-space_wf,
real_wf,
rv-mul_wf,
real-vector-space_subtype1,
ss-sep_wf,
rv-0_wf,
rv-mul0
Rules used in proof :
productElimination,
independent_functionElimination,
independent_isectElimination,
natural_numberEquality,
voidElimination,
isect_memberEquality,
applyEquality,
because_Cache,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[a:\mBbbR{}]. a*0 \mequiv{} 0
Date html generated:
2016_11_08-AM-09_14_05
Last ObjectModification:
2016_11_01-PM-01_10_11
Theory : inner!product!spaces
Home
Index