
theorem
for R being degenerated Ring,
    p being Polynomial of R
holds {i where i is Nat : p.i <> 0.R} = {}
proof
let R be degenerated Ring, p be Polynomial of R;
A:now let i be Nat;
 thus p.i = p.i * 1.R .= p.i * 0.R by STRUCT_0:def 8 .= 0.R;
 end;
set M = {i where i is Nat : p.i <> 0.R};
now assume B: M <> {};
  let x be Element of M;
  x in M by B;
  then consider j being Nat such that H1: j = x & p.j <> 0.R;
  thus contradiction by H1,A;
  end;
hence thesis;
end;
