Nuprl Lemma : rv-sub_wf
∀[rv:RealVectorSpace]. ∀[x,y:Point]. (x - y ∈ Point)
Proof
Definitions occuring in Statement :
rv-sub: x - y,
real-vector-space: RealVectorSpace,
ss-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
rv-sub: x - y,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real-vector-space_wf,
real-vector-space_subtype1,
ss-point_wf,
rv-minus_wf,
rv-add_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
applyEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[x,y:Point]. (x - y \mmember{} Point)
Date html generated:
2016_11_08-AM-09_15_22
Last ObjectModification:
2016_10_31-PM-03_22_27
Theory : inner!product!spaces
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