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 Th59:
  Eval(Leading-Monomial p) = p.(len p-'1) (#) #Z(len p-'1)
  proof
    set l = Leading-Monomial p;
    set m = len p-'1;
    set f = p.m (#) #Z(m);
    Eval(l) = f
    proof
      let r be Element of REAL;
A1:   power(In(r,F),m) = r |^ m by Th39
      .= r #Z m by PREPOWER:36
      .= ( #Z m).r by TAYLOR_1:def 1;
      thus (Eval(l)).r = eval(l,In(r,F)) by POLYNOM5:def 13
      .= p.m * power(In(r,F),m) by POLYNOM4:22
      .= f.r by A1,VALUED_1:6;
    end;
    hence thesis;
  end;
