Nuprl Lemma : rv-sub-sep
∀rv:RealVectorSpace. ∀x,x',y,y':Point. (x - y # x' - y' ⇒ (x # x' ∨ y # y'))
Proof
Definitions occuring in Statement :
rv-sub: x - y,
real-vector-space: RealVectorSpace,
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
rv-sub: x - y,
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
rv-minus: -x,
uimplies: b supposing a,
false: False
Lemmas referenced :
rv-add-sep,
rv-minus_wf,
ss-sep_wf,
real-vector-space_subtype1,
rv-sub_wf,
ss-point_wf,
real-vector-space_wf,
int-to-real_wf,
rv-mul-sep,
rneq_irreflexivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
unionElimination,
inlFormation,
applyEquality,
because_Cache,
sqequalRule,
inrFormation,
minusEquality,
natural_numberEquality,
independent_isectElimination,
voidElimination
Latex:
\mforall{}rv:RealVectorSpace. \mforall{}x,x',y,y':Point. (x - y \# x' - y' {}\mRightarrow{} (x \# x' \mvee{} y \# y'))
Date html generated:
2017_10_04-PM-11_51_17
Last ObjectModification:
2017_06_27-AM-10_46_13
Theory : inner!product!spaces
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