
theorem c20:
for R being preordered non degenerated Ring,
    P being Preordering of R holds 0.R <P, 1.R & -1.R <P, 0.R
proof
let R be preordered non degenerated Ring, P be Preordering of R;
0.R <=P, 1.R by REALALG1:25;
hence 0.R <P, 1.R;
-1.R <=P, 0.R by REALALG1:25;
hence -1.R <P, 0.R;
end;
