reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real,
  s,t,h,z,z1,z2,z3,s1,s2,s3 for Complex;

theorem
  (for z being Complex holds Polynom(a,b,c,d,z) = Polynom(a9,b9,
  c9,d9,z ) ) implies a = a9 & b = b9 & c = c9 & d = d9
proof
  assume
A1: for z being Complex holds Polynom(a,b,c,d,z) = Polynom(a9,b9,
  c9,d9,z);
  then
A2: Polynom(a,b,c,d,0) = Polynom(a9,b9,c9,d9,0);
A3: Polynom(a,b,c,d,1) = Polynom(a9,b9,c9,d9,1) & Polynom(a,b,c,d,-1) =
  Polynom( a9,b9,c9,d9,-1) by A1;
A4: Polynom(a,b,c,d,2) = Polynom(a9,b9,c9,d9,2) by A1;
  hence a = a9 by A2,A3;
  thus b = b9 by A2,A3;
  thus c = c9 by A2,A3,A4;
  thus thesis by A2;
end;
