Nuprl Lemma : vs-subtract_wf

∀[K:RngSig]. ∀[vs:VectorSpace(K)]. ∀[x,y:Point(vs)].  ((x - y) ∈ Point(vs))


Proof




Definitions occuring in Statement :  vs-subtract: (x - y),  vector-space: VectorSpace(K),  vs-point: Point(vs),  uall: ∀[x:A]. B[x],  member: t ∈ T,  rng_sig: RngSig
Definitions unfolded in proof :  all: ∀x:A. B[x],  vs-subtract: (x - y),  member: t ∈ T,  uall: ∀[x:A]. B[x]
Lemmas referenced :  rng_sig_wf,  vector-space_wf,  vs-point_wf,  rng_one_wf,  rng_minus_wf,  vs-mul_wf,  vs-add_wf
Rules used in proof :  dependent_functionElimination,  because_Cache,  isect_memberEquality,  equalitySymmetry,  equalityTransitivity,  axiomEquality,  hypothesis,  applyEquality,  hypothesisEquality,  thin,  isectElimination,  sqequalHypSubstitution,  extract_by_obid,  sqequalRule,  cut,  introduction,  isect_memberFormation,  sqequalReflexivity,  computationStep,  sqequalTransitivity,  sqequalSubstitution

Latex:
\mforall{}[K:RngSig].  \mforall{}[vs:VectorSpace(K)].  \mforall{}[x,y:Point(vs)].    ((x  -  y)  \mmember{}  Point(vs))



Date html generated: 2018_05_22-PM-09_42_53
Last ObjectModification: 2018_01_09-PM-02_06_37

Theory : linear!algebra


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