let p, q, r be Element of (Polynom-Ring L); :: according to GROUP_1:def 4 :: thesis: (p * q) * r = p * (q * r)
reconsider p1 = p, q1 = q, r1 = r as sequence of L by Def12;
A1: q * r = q1 *' r1 by Def12;
p * q = p1 *' q1 by Def12;
hence (p * q) * r = (p1 *' q1) *' r1 by Def12
.= p1 *' (q1 *' r1) by Th34
.= p * (q * r) by A1, Def12 ;
:: thesis: verum