Nuprl Lemma : rv-mul-sep
∀rv:RealVectorSpace. ∀a,b:ℝ. ∀x,y:Point. (a*x # b*y ⇒ (a ≠ b ∨ x # y))
Proof
Definitions occuring in Statement :
rv-mul: a*x,
real-vector-space: RealVectorSpace,
ss-sep: x # y,
ss-point: Point,
rneq: x ≠ y,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
rv-mul: a*x,
or: P ∨ Q,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
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,
all: ∀x:A. B[x]
Lemmas referenced :
real-vector-space_wf,
rneq_wf,
radd_wf,
rmul_wf,
int-to-real_wf,
real_wf,
or_wf,
ss-sep_wf,
ss-eq_wf,
all_wf,
ss-point_wf,
subtype_rel_self
Rules used in proof :
natural_numberEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
functionExtensionality,
lambdaEquality,
productEquality,
because_Cache,
functionEquality,
setEquality,
isectElimination,
extract_by_obid,
tokenEquality,
applyEquality,
hypothesis,
cut,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}rv:RealVectorSpace. \mforall{}a,b:\mBbbR{}. \mforall{}x,y:Point. (a*x \# b*y {}\mRightarrow{} (a \mneq{} b \mvee{} x \# y))
Date html generated:
2016_11_08-AM-09_13_40
Last ObjectModification:
2016_11_02-PM-00_46_01
Theory : inner!product!spaces
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