Nuprl Lemma : rv-mul-linear
∀[rv:RealVectorSpace]. ∀[a:ℝ]. ∀[x,y:Point]. a*x + y ≡ a*x + a*y
Proof
Definitions occuring in Statement :
rv-mul: a*x,
rv-add: x + y,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
ss-point: Point,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
false: False,
not: ¬A,
ss-eq: x ≡ y,
sq_stable: SqStable(P),
squash: ↓T,
rv-add: x + y,
rv-mul: a*x,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
real-vector-space: RealVectorSpace,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real-vector-space_wf,
rv-add_wf,
rv-mul_wf,
real-vector-space_subtype1,
sq_stable__ss-eq,
rneq_wf,
radd_wf,
rmul_wf,
int-to-real_wf,
real_wf,
ss-sep_wf,
ss-eq_wf,
all_wf,
ss-point_wf,
subtype_rel_self
Rules used in proof :
voidElimination,
isect_memberEquality,
dependent_functionElimination,
independent_functionElimination,
productElimination,
imageElimination,
baseClosed,
imageMemberEquality,
Error :applyLambdaEquality,
natural_numberEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
functionExtensionality,
lambdaEquality,
productEquality,
because_Cache,
functionEquality,
setEquality,
isectElimination,
extract_by_obid,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[a:\mBbbR{}]. \mforall{}[x,y:Point]. a*x + y \mequiv{} a*x + a*y
Date html generated:
2016_11_08-AM-09_13_57
Last ObjectModification:
2016_10_31-PM-06_09_03
Theory : inner!product!spaces
Home
Index