theorem
  S is (R4) (R8) (R13) implies a * (b * a)" <<>> b"
  proof
    assume
A1: S is (R4) (R8) (R13);
    take b"*(b*(a*(b*a)"));
    thus b"*(b*(a*(b*a)")) =*=> a*(b*a)" by A1,Th2;
    b"*(b*(a*(b*a)")) ==> b"*1.S & b"*1.S ==> b" by A1,ThI3;
    hence b"*(b*(a*(b*a)")) =*=> b" by Lem3;
  end;
