
theorem
  REAL * = the set of all X where X is FinSequence of REAL
  proof
    now
      now
        let x be object;
        assume x in REAL *;
        then x is FinSequence of REAL by FINSEQ_1:def 11;
        hence x in the set of all X where X is FinSequence of REAL;
      end;
      hence REAL * c= the set of all X where X is FinSequence of REAL;
      now
        let x be object;
        assume x in the set of all X where X is FinSequence of REAL;
        then ex X be FinSequence of REAL st x = X;
        hence x in REAL * by FINSEQ_1:def 11;
      end;
      hence the set of all X where X is FinSequence of REAL c= REAL *;
    end;
    hence thesis;
  end;
