
theorem c5:
for R being preordered Ring,
    P being Preordering of R,
    a,b,c being Element of R st a <= P,b & 0.R <=P, c 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 & 0.R <=P, c;
then a <=_(OrdRel P), b & 0.R <=_(OrdRel P), c;
hence thesis by lemOP,REALALG1:def 4;
end;
