
theorem
for F being preordered Field,
    P being Preordering of F
for a being non zero P-ordered Element of F,
    b being P-ordered Element of F holds abs(P,b*a") = abs(P,b) * abs(P,a)"
proof
let F be preordered Field, P be Preordering of F,
    a be non zero P-ordered Element of F, b be P-ordered Element of F;
thus abs(P,b*a") = abs(P,b) * abs(P,a") by abs10
                .= abs(P,b) * abs(P,a)" by sq2;
end;
