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 Th60:
  for r being Element of F_Real holds Eval(seq(n,r)) = r (#) #Z n
  proof
    let r be Element of F_Real;
    let a be Element of REAL;
    set p = seq(n,r);
    set x = In(a,F);
A1: p.n = r by Th24;
A2: power(x,n) = ( #Z n).a by Th43;
    thus (Eval(p)).a = eval(p,x) by POLYNOM5:def 13
    .= p.n * power(x,n) by Th38
    .= (r (#) #Z n).a by A1,A2,VALUED_1:6;
  end;
