let p, q, r be Element of (Formal-Series (n,L)); :: according to GROUP_1:def 3 :: thesis: (p * q) * r = p * (q * r)
reconsider p1 = p, q1 = q, r1 = r as Series of n,L by Def3;
A2: 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 POLYNOM1:27
.= p * (q * r) by A2, Def3 ;
:: thesis: verum