Nuprl Lemma : sq_stable__rv-sep-ext

∀rv:InnerProductSpace. ∀x,y:Point.  SqStable(x # y)


Proof




Definitions occuring in Statement :  inner-product-space: InnerProductSpace,  ss-sep: x # y,  ss-point: Point,  sq_stable: SqStable(P),  all: ∀x:A. B[x]
Definitions unfolded in proof :  any: any x,  rv-norm-positive-iff-ext,  ss-sep-or,  ss-sep_functionality,  so_apply: x[s1;s2],  so_lambda: λ2x y.t[x; y],  squash: ↓T,  or: P ∨ Q,  guard: {T},  prop: ℙ,  has-value: (a)↓,  implies: P ⇒ Q,  all: ∀x:A. B[x],  and: P ∧ Q,  strict4: strict4(F),  uimplies: b supposing a,  top: Top,  so_apply: x[s1;s2;s3;s4],  so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),  uall: ∀[x:A]. B[x],  rv-add-sep,  rv-add-sep2,  rv-sep-iff,  experimental: experimental{impliesFunctionality}(possibleextract),  sq_stable__rv-sep,  member: t ∈ T
Lemmas referenced :  strict4-spread,  is-exception_wf,  base_wf,  has-value_wf_base,  lifting-strict-spread,  sq_stable__rv-sep,  rv-norm-positive-iff-ext,  ss-sep-or,  ss-sep_functionality,  rv-add-sep,  rv-add-sep2,  rv-sep-iff
Rules used in proof :  equalitySymmetry,  equalityTransitivity,  because_Cache,  inlFormation,  exceptionSqequal,  imageElimination,  imageMemberEquality,  inrFormation,  applyExceptionCases,  hypothesisEquality,  closedConclusion,  baseApply,  callbyvalueApply,  lambdaFormation,  independent_pairFormation,  independent_isectElimination,  voidEquality,  voidElimination,  isect_memberEquality,  baseClosed,  isectElimination,  sqequalHypSubstitution,  thin,  sqequalRule,  hypothesis,  extract_by_obid,  instantiate,  cut,  sqequalReflexivity,  computationStep,  sqequalTransitivity,  sqequalSubstitution,  introduction

Latex:
\mforall{}rv:InnerProductSpace.  \mforall{}x,y:Point.    SqStable(x  \#  y)



Date html generated: 2016_11_08-AM-09_16_36
Last ObjectModification: 2016_11_03-AM-10_58_19

Theory : inner!product!spaces


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