let R be non degenerated comRing; (BSFSeri R) . (1. (Formal-Series (1,R))) = 1. (Formal-Series R)
consider e1 being Series of 1,R such that
A1:
( e1 = 1. (Formal-Series (1,R)) & (BSFSeri R) . (1. (Formal-Series (1,R))) = e1 * NBag1 )
by Def4;
e1 = 1_ (1,R)
by A1, Def3;
then (BSFSeri R) . (1. (Formal-Series (1,R))) =
((0_ (1,R)) +* ((EmptyBag 1),(1. R))) * NBag1
by A1
.=
1_. R
by Th23
.=
1. (Formal-Series R)
by POLYALG1:def 2
;
hence
(BSFSeri R) . (1. (Formal-Series (1,R))) = 1. (Formal-Series R)
; verum