theorem
  S is (R2) (R9) implies a * (a") <<>> 1.S
  proof
    assume
A1: S is (R2) (R9);
    take a""*a";
    a"" ==> a by A1;
    hence a""*a" =*=> a*a" by Th2,ThI2;
    thus a""*a" =*=> 1.S by A1,Th2;
  end;
