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Step * of Lemma mul_over_plus_fps

No Annotations
∀[X:Type]
  ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[a,b,c:PowerSeries(X;r)].
    (((a*(b+c)) = ((a*b)+(a*c)) ∈ PowerSeries(X;r)) ∧ (((b+c)*a) = ((b*a)+(c*a)) ∈ PowerSeries(X;r))) 
  supposing valueall-type(X)
BY
{ (RepeatFor 3 ((D 0 THENA Auto))
   THEN (ProveSpecializedLemmaWReduce rng_times_over_plus) 1 [⌜parm{i}⌝;⌜⌜fps-rng(r)⌝⌝]⋅
   ) }

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Latex:

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Latex:
No  Annotations
\mforall{}[X:Type]
    \mforall{}[eq:EqDecider(X)].  \mforall{}[r:CRng].  \mforall{}[a,b,c:PowerSeries(X;r)].
        (((a*(b+c))  =  ((a*b)+(a*c)))  \mwedge{}  (((b+c)*a)  =  ((b*a)+(c*a)))) 
    supposing  valueall-type(X)


By

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Latex:
(RepeatFor  3  ((D  0  THENA  Auto))
  THEN  (ProveSpecializedLemmaWReduce  rng\_times\_over\_plus)  1  [\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}\mkleeneopen{}fps-rng(r)\mkleeneclose{}\mkleeneclose{}]\mcdot{}
  )

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