
theorem lemPP:
for F being ordered Field,
    P being Ordering of F
for E being Field st E == F holds
E is ordered & ex Q being Subset of E st Q = P & Q is positive_cone
proof
let F be ordered Field, P be Ordering of F, E be Field;
assume AS: E == F; then
A: E is Subring of F by FIELD_5:12;
hence E is ordered;
reconsider K = E as ordered Field by A;
P /\ (the carrier of K) is Ordering of K by A,REALALG1:34;
hence thesis by AS,XBOOLE_1:28;
end;
