Nuprl Lemma : ip-strict-between_wf

∀[rv:InnerProductSpace]. ∀[a,b,c:Point].  (a-b-c ∈ ℙ)


Proof




Definitions occuring in Statement :  ip-strict-between: a-b-c,  inner-product-space: InnerProductSpace,  ss-point: Point,  uall: ∀[x:A]. B[x],  prop: ℙ,  member: t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  ip-strict-between: a-b-c,  prop: ℙ,  and: P ∧ Q,  subtype_rel: A ⊆r B,  guard: {T},  uimplies: b supposing a
Lemmas referenced :  ip-between_wf,  ss-sep_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,  sqequalRule,  productEquality,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  hypothesis,  applyEquality,  because_Cache,  axiomEquality,  equalityTransitivity,  equalitySymmetry,  instantiate,  independent_isectElimination,  isect_memberEquality

Latex:
\mforall{}[rv:InnerProductSpace].  \mforall{}[a,b,c:Point].    (a-b-c  \mmember{}  \mBbbP{})



Date html generated: 2017_10_05-AM-00_03_31
Last ObjectModification: 2017_03_12-PM-02_12_25

Theory : inner!product!spaces


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