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Step * 6 of Lemma fps-deriv-compose


1. X : Type
2. valueall-type(X)
3. eq : EqDecider(X)
4. r : CRng
5. f : PowerSeries(X;r)
6. g : PowerSeries(X;r)
7. x : X
8. λ2f.df(x:=g)/dx = λ2f.(df/dx(x:=g)*dg/dx) ∈ (PowerSeries(X;r) ⟶ PowerSeries(X;r))
⊢ df(x:=g)/dx = (df/dx(x:=g)*dg/dx) ∈ PowerSeries(X;r)
BY
{ (ApFunToHypEquands `Z' ⌜Z[f]⌝ ⌜PowerSeries(X;r)⌝ (-1)⋅ THEN Auto) }

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Latex:

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Latex:

1.  X  :  Type
2.  valueall-type(X)
3.  eq  :  EqDecider(X)
4.  r  :  CRng
5.  f  :  PowerSeries(X;r)
6.  g  :  PowerSeries(X;r)
7.  x  :  X
8.  \mlambda{}\msubtwo{}f.df(x:=g)/dx  =  \mlambda{}\msubtwo{}f.(df/dx(x:=g)*dg/dx)
\mvdash{}  df(x:=g)/dx  =  (df/dx(x:=g)*dg/dx)


By

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Latex:
(ApFunToHypEquands  `Z'  \mkleeneopen{}Z[f]\mkleeneclose{}  \mkleeneopen{}PowerSeries(X;r)\mkleeneclose{}  (-1)\mcdot{}  THEN  Auto)

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