theorem
  S is (R12) (R15) implies a * (b * a)" =*=> b"
  proof
    assume
A1: S is (R12) (R15);
    a * (b * a)" ==> a*(a"*b") & a*(a"*b") ==> b" by A1,ThI3;
    hence a * (b * a)" =*=> b" by Lem3;
  end;
