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Step * of Lemma radd-list-linearity1

∀[T:Type]. ∀[x,y:T ⟶ ℝ]. ∀[L:T List].
  (radd-list(map(λk.(x[k] + y[k]);L)) = (radd-list(map(λk.x[k];L)) + radd-list(map(λk.y[k];L))))
BY
{ (InductionOnList THEN Reduce 0 THEN (RWW "radd-list-cons -1" 0 THENA Auto) THEN slowRNorm 0 THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[x,y:T  {}\mrightarrow{}  \mBbbR{}].  \mforall{}[L:T  List].
    (radd-list(map(\mlambda{}k.(x[k]  +  y[k]);L))  =  (radd-list(map(\mlambda{}k.x[k];L))  +  radd-list(map(\mlambda{}k.y[k];L))))


By

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Latex:
(InductionOnList
  THEN  Reduce  0
  THEN  (RWW  "radd-list-cons  -1"  0  THENA  Auto)
  THEN  slowRNorm  0
  THEN  Auto)

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