Nuprl Lemma : select-qv-mul

∀[as:Top List]. ∀[r:Top]. ∀[i:ℕdimension(as)].  (qv-mul(r;as)[i] ~ r * as[i])


Proof




Definitions occuring in Statement :  qv-mul: qv-mul(r;bs),  qv-dim: dimension(as),  qmul: r * s,  select: L[n],  list: T List,  int_seg: {i..j-},  uall: ∀[x:A]. B[x],  top: Top,  natural_number: $n,  sqequal: s ~ t
Definitions unfolded in proof :  qv-dim: dimension(as),  uall: ∀[x:A]. B[x],  member: t ∈ T,  qv-mul: qv-mul(r;bs),  top: Top
Lemmas referenced :  select-map,  int_seg_wf,  length_wf,  top_wf,  list_wf
Rules used in proof :  sqequalSubstitution,  sqequalRule,  sqequalReflexivity,  sqequalTransitivity,  computationStep,  isect_memberFormation,  introduction,  cut,  lemma_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  isect_memberEquality,  voidElimination,  voidEquality,  hypothesisEquality,  hypothesis,  sqequalAxiom,  natural_numberEquality,  because_Cache

Latex:
\mforall{}[as:Top  List].  \mforall{}[r:Top].  \mforall{}[i:\mBbbN{}dimension(as)].    (qv-mul(r;as)[i]  \msim{}  r  *  as[i])



Date html generated: 2016_05_15-PM-11_20_47
Last ObjectModification: 2015_12_27-PM-07_33_04

Theory : rationals


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