Step
*
5
1
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. b : bag(X)
⊢ d<b>(x:=g)/dx = (d<b>/dx(x:=g)*dg/dx) ∈ PowerSeries(X;r)
BY
{ (RWW "fps-deriv-single fps-compose-scalar-mul" 0 THENA Auto) }
1
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. b : bag(X)
⊢ d<b>(x:=g)/dx = ((int-to-ring(r;(#x in b)))*<bag-drop(eq;b;x)>(x:=g)*dg/dx) ∈ PowerSeries(X;r)
Latex:
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. b : bag(X)
\mvdash{} d<b>(x:=g)/dx = (d<b>/dx(x:=g)*dg/dx)
By
Latex:
(RWW "fps-deriv-single fps-compose-scalar-mul" 0 THENA Auto)
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