
theorem poly3:
for L being associative non empty multMagma,
    p being sequence of L,
    a,b being Element of L holds (a * b) * p = a * (b * p)
proof
let L be associative non empty multMagma,
    p being sequence of L, a,b being Element of L;
now let x be object;
  assume x in NAT;
  then reconsider i = x as Element of NAT;
  thus ((a * b) * p).x = (a * b) * (p.i) by POLYNOM5:def 4
                      .= a * (b * (p.i)) by GROUP_1:def 3
                      .= a * ((b * p).i) by POLYNOM5:def 4
                      .= (a * (b * p)).x by POLYNOM5:def 4;
  end;
hence thesis by FUNCT_2:12;
end;
