Step
*
1
3
of Lemma
KozenSilva-lemma
1. r : CRng
2. x : Atom
3. y : Atom
4. h : PowerSeries(r)
5. n : ℕ
6. m : ℕ
7. n ≤ m
8. ¬(x = y ∈ Atom)
9. fps-ucont(Atom;AtomDeq;r;f.[([f]_n(y:=1)*Δ(x,y))]_m)
10. fps-ucont(Atom;AtomDeq;r;f.([f]_n(y:=(atom(x)+atom(y)))*((atom(x)+atom(y)))^(m - n)))
11. f : PowerSeries(r)
12. g : PowerSeries(r)
⊢ [([(f+g)]_n(y:=1)*Δ(x,y))]_m = ([([f]_n(y:=1)*Δ(x,y))]_m+[([g]_n(y:=1)*Δ(x,y))]_m) ∈ PowerSeries(r)
BY
{ xxx((RWO "fps-set-to-one-add" 0 THENA Auto) THEN FpsNorm 0 THEN Auto THEN RWO "fps-add-slice" 0 THEN Auto)xxx }
Latex:
Latex:
1. r : CRng
2. x : Atom
3. y : Atom
4. h : PowerSeries(r)
5. n : \mBbbN{}
6. m : \mBbbN{}
7. n \mleq{} m
8. \mneg{}(x = y)
9. fps-ucont(Atom;AtomDeq;r;f.[([f]\_n(y:=1)*\mDelta{}(x,y))]\_m)
10. fps-ucont(Atom;AtomDeq;r;f.([f]\_n(y:=(atom(x)+atom(y)))*((atom(x)+atom(y)))\^{}(m - n)))
11. f : PowerSeries(r)
12. g : PowerSeries(r)
\mvdash{} [([(f+g)]\_n(y:=1)*\mDelta{}(x,y))]\_m = ([([f]\_n(y:=1)*\mDelta{}(x,y))]\_m+[([g]\_n(y:=1)*\mDelta{}(x,y))]\_m)
By
Latex:
xxx((RWO "fps-set-to-one-add" 0 THENA Auto)
THEN FpsNorm 0
THEN Auto
THEN RWO "fps-add-slice" 0
THEN Auto)xxx
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