
theorem c4:
for R being preordered Ring,
    P being Preordering of R,
    a,b,c being Element of R st a <=P, b holds a+c <=P, b+c
proof
let R be preordered Ring, P be Preordering of R, a,b,c be Element of R;
assume a <= P, b;
then a <=_(OrdRel P), b;
hence thesis by lemOP,REALALG1:def 3;
end;
