reserve z,z1,z2,z3,z4 for Element of F_Complex;

theorem
  for n be non zero Element of NAT for x be Element of F_Complex for v
  be CRoot of n,x st v = 0.F_Complex holds x = 0.F_Complex
proof
  let n be non zero Element of NAT;
  let x be Element of F_Complex;
  let v be CRoot of n,x;
  assume v = 0.F_Complex;
  then (power F_Complex).(0.F_Complex,n) = x by Def2;
  hence thesis by NAT_1:3,VECTSP_1:36;
end;
