theorem
  S is (R1) (R2) (R3) implies a" * (a * b) <<>> b
  proof
    assume
A1: S is (R1) (R2) (R3);
    take (a"*a)*b;
    thus (a"*a)*b =*=> a"*(a*b) by A1,Th2;
    (a"*a)*b ==> 1.S * b & 1.S * b ==> b by A1,ThI2; then
    (a"*a)*b =*=> 1.S * b & 1.S * b =*=> b by Th2;
    hence (a"*a)*b =*=> b by Th3;
  end;
