Nuprl Lemma : rv-mul-sep1
∀rv:RealVectorSpace. ∀a,b:ℝ. ∀y:Point. (a*y # b*y ⇒ a ≠ b)
Proof
Definitions occuring in Statement :
rv-mul: a*x,
real-vector-space: RealVectorSpace,
rneq: x ≠ y,
real: ℝ,
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
rv-mul-sep,
ss-sep_wf,
real-vector-space_subtype1,
rv-mul_wf,
ss-point_wf,
real_wf,
real-vector-space_wf,
ss-sep-irrefl
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
applyEquality,
sqequalRule,
because_Cache,
unionElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}rv:RealVectorSpace. \mforall{}a,b:\mBbbR{}. \mforall{}y:Point. (a*y \# b*y {}\mRightarrow{} a \mneq{} b)
Date html generated:
2017_10_04-PM-11_50_22
Last ObjectModification:
2017_08_10-PM-03_38_14
Theory : inner!product!spaces
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