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 Th52:
  Eval(0_.F_Real) = REAL --> 0
  proof
    Eval(z) = REAL --> r0
    proof
      let r be Element of REAL;
      thus (Eval(z)).r = eval(z,In(r,F)) by POLYNOM5:def 13
      .= r0 by POLYNOM4:17
      .= (REAL --> r0).r;
    end;
    hence thesis;
  end;
