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Step * of Lemma vs-lift-zero-bfs

∀[K:Rng]. ∀[S:Type]. ∀[ss:bag(S)]. ∀[vs:VectorSpace(K)]. ∀[f:S ⟶ Point(vs)].  (vs-lift(vs;f;0 * ss) = 0 ∈ Point(vs))
BY
{ (Auto
   THEN RepUR ``vs-lift vs-bag-add zero-bfs`` 0
   THEN (RWW "bag-summation-map" 0 THENA Auto)
   THEN Reduce 0
   THEN Fold `vs-bag-add` 0
   THEN RWO "vs-bag-add-mul<" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[K:Rng].  \mforall{}[S:Type].  \mforall{}[ss:bag(S)].  \mforall{}[vs:VectorSpace(K)].  \mforall{}[f:S  {}\mrightarrow{}  Point(vs)].
    (vs-lift(vs;f;0  *  ss)  =  0)


By

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Latex:
(Auto
  THEN  RepUR  ``vs-lift  vs-bag-add  zero-bfs``  0
  THEN  (RWW  "bag-summation-map"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  Fold  `vs-bag-add`  0
  THEN  RWO  "vs-bag-add-mul<"  0
  THEN  Auto)

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