Nuprl Lemma : stable__ip-between
∀[rv:InnerProductSpace]. ∀[a,b,c:Point]. Stable{a_b_c}
Proof
Definitions occuring in Statement :
ip-between: a_b_c,
inner-product-space: InnerProductSpace,
ss-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ip-between: a_b_c,
subtype_rel: A ⊆r B,
stable: Stable{P},
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
stable_req,
radd_wf,
rmul_wf,
rv-norm_wf,
rv-sub_wf,
rv-ip_wf,
int-to-real_wf,
req_witness,
not_wf,
ip-between_wf,
ss-point_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
natural_numberEquality,
isect_memberEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
independent_isectElimination
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,c:Point]. Stable\{a\_b\_c\}
Date html generated:
2017_10_04-PM-11_59_51
Last ObjectModification:
2017_03_09-PM-02_36_04
Theory : inner!product!spaces
Home
Index