let p, q, r be Element of (Formal-Series (n,L)); :: according to RLVECT_1:def 3 :: thesis: (p + q) + r = p + (q + r)
reconsider p1 = p, q1 = q, r1 = r as Series of n,L by Def3;
A1: q + r = q1 + r1 by Def3;
p + q = p1 + q1 by Def3;
hence (p + q) + r = (p1 + q1) + r1 by Def3
.= p1 + (q1 + r1) by POLYNOM1:21
.= p + (q + r) by A1, Def3 ;
:: thesis: verum