reserve n for Nat;

theorem lem1:
for n being even Nat,
    x being Element of F_Real holds eval(npoly(F_Real,n),x) > 0.F_Real
proof
let n be even Nat, x be Element of F_Real;
per cases;
suppose n = 0;
  hence thesis by lem1e;
  end;
suppose S: n is non zero;
  x|^n + 1 >= 0.F_Real + 1 by XX,XREAL_1:6;
  then x|^n + 1.F_Real >= 1;
  hence thesis by lem1a,S;
  end;
end;
