Nuprl Lemma : rv-mul_functionality
∀[rv:RealVectorSpace]. ∀[a,b:ℝ]. ∀[x,x':Point]. (a*x ≡ b*x') supposing (x ≡ x' and (a = b))
Proof
Definitions occuring in Statement :
rv-mul: a*x,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
ss-point: Point,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
guard: {T},
rneq: x ≠ y,
false: False,
prop: ℙ,
or: P ∨ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
ss-eq: x ≡ y,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
req_inversion,
rless_irreflexivity,
rleq_weakening,
rless_transitivity1,
real-vector-space_wf,
real_wf,
ss-point_wf,
req_wf,
ss-eq_wf,
ss-sep_wf,
rv-mul-sep1,
rv-mul-sep2,
rv-mul_wf,
real-vector-space_subtype1,
ss-sep-or
Rules used in proof :
independent_isectElimination,
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
lambdaEquality,
because_Cache,
unionElimination,
independent_functionElimination,
isectElimination,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[a,b:\mBbbR{}]. \mforall{}[x,x':Point]. (a*x \mequiv{} b*x') supposing (x \mequiv{} x' and (a = b))
Date html generated:
2016_11_08-AM-09_13_54
Last ObjectModification:
2016_10_31-PM-06_27_24
Theory : inner!product!spaces
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