Nuprl Lemma : rv-mul_wf
∀[rv:RealVectorSpace]. ∀[a:ℝ]. ∀[x:Point]. (a*x ∈ Point)
Proof
Definitions occuring in Statement :
rv-mul: a*x,
real-vector-space: RealVectorSpace,
ss-point: Point,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
all: ∀x:A. B[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
and: P ∧ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
record-select: r.x,
record+: record+,
real-vector-space: RealVectorSpace,
rv-mul: a*x,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real-vector-space_wf,
rmul_wf,
int-to-real_wf,
req_wf,
real_wf,
ss-eq_wf,
all_wf,
ss-point_wf,
subtype_rel_self,
real-vector-space_subtype1
Rules used in proof :
isect_memberEquality,
axiomEquality,
natural_numberEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
functionExtensionality,
lambdaEquality,
productEquality,
because_Cache,
functionEquality,
setEquality,
isectElimination,
tokenEquality,
thin,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
applyEquality,
hypothesisEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[a:\mBbbR{}]. \mforall{}[x:Point]. (a*x \mmember{} Point)
Date html generated:
2016_11_08-AM-09_13_37
Last ObjectModification:
2016_10_31-PM-01_45_25
Theory : inner!product!spaces
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