Nuprl Lemma : rv-add-sep1
∀rv:RealVectorSpace. ∀x,x',y:Point. (x + y # x' + y ⇒ x # x')
Proof
Definitions occuring in Statement :
rv-add: x + y,
real-vector-space: RealVectorSpace,
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-add-sep,
ss-sep_wf,
real-vector-space_subtype1,
rv-add_wf,
ss-point_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{}x,x',y:Point. (x + y \# x' + y {}\mRightarrow{} x \# x')
Date html generated:
2017_10_04-PM-11_50_16
Last ObjectModification:
2017_08_10-PM-03_38_11
Theory : inner!product!spaces
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