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Step * of Lemma vs-lift-bfs-equiv

∀[K:Rng]. ∀[S:Type]. ∀[as,bs:basic-formal-sum(K;S)].
  ∀[vs:VectorSpace(K)]. ∀[f:S ⟶ Point(vs)].  (vs-lift(vs;f;as) = vs-lift(vs;f;bs) ∈ Point(vs)) 
  supposing bfs-equiv(K;S;as;bs)
BY
{ (Auto
   THEN (InstLemma `bfs-equiv-implies` [⌜S⌝;⌜K⌝;⌜λas,bs. (vs-lift(vs;f;as) = vs-lift(vs;f;bs) ∈ Point(vs))⌝]⋅ THENA Auto\000C)
   THEN All Reduce
   THEN EAuto 1) }

1
1. K : Rng
2. S : Type
3. as : basic-formal-sum(K;S)
4. bs : basic-formal-sum(K;S)
5. bfs-equiv(K;S;as;bs)
6. vs : VectorSpace(K)
7. f : S ⟶ Point(vs)
⊢ EquivRel(basic-formal-sum(K;S);x,y.vs-lift(vs;f;x) = vs-lift(vs;f;y) ∈ Point(vs))

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Latex:

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Latex:
\mforall{}[K:Rng].  \mforall{}[S:Type].  \mforall{}[as,bs:basic-formal-sum(K;S)].
    \mforall{}[vs:VectorSpace(K)].  \mforall{}[f:S  {}\mrightarrow{}  Point(vs)].    (vs-lift(vs;f;as)  =  vs-lift(vs;f;bs)) 
    supposing  bfs-equiv(K;S;as;bs)


By

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Latex:
(Auto
  THEN  (InstLemma  `bfs-equiv-implies`  [\mkleeneopen{}S\mkleeneclose{};\mkleeneopen{}K\mkleeneclose{};\mkleeneopen{}\mlambda{}as,bs.  (vs-lift(vs;f;as)  =  vs-lift(vs;f;bs))\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  THEN  All  Reduce
  THEN  EAuto  1)

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