reserve X for non empty BCIStr_1;
reserve d for Element of X;
reserve n,m,k for Nat;
reserve f for sequence of  the carrier of X;

theorem Th32:
  for X being BCI-Algebra_with_Condition(S) holds for a1,a2 being
  Element of X holds Product_S<*a1,a2*> = a1 * a2
proof
  let X be BCI-Algebra_with_Condition(S);
  let a1,a2 be Element of X;
  thus Product_S<*a1,a2*> = Product_S<*a1*> * a2 by Th18,FINSOP_1:4
    .= a1 * a2 by FINSOP_1:11;
end;
