reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;
reserve f,g for differentiable Function of REAL,REAL;
reserve L for non empty ZeroStr;
reserve x for Element of L;
reserve p,q for Polynomial of F_Real;

theorem Th53:
  for r being Element of F_Real holds Eval(<%r%>) = REAL --> r
  proof
    let r be Element of F;
    Eval(<%r%>) = REAL --> In(r,REAL)
    proof
      let a be Element of REAL;
      thus (Eval(<%r%>)).a = eval(<%r%>,In(a,F)) by POLYNOM5:def 13
      .= r by POLYNOM5:37
      .= (REAL --> In(r,REAL)).a;
    end;
    hence thesis;
  end;
