
theorem c2:
for R being preordered Ring,
    P being Preordering of R,
    a,b being Element of R st a <=P, b & b <=P, a holds a = b
proof
let R be preordered Ring, P be Preordering of R;
let a,b be Element of R;
assume a <=P, b & b <=P, a;
then a <=_(OrdRel P), b & b <=_(OrdRel P), a;
hence thesis by REALALG1:2;
end;
