
theorem
for F being Field st Char F <> 2
holds F is formally_real iff ex P being Subset of F st P is prepositive_cone
proof
let F be Field;
assume AS: Char F <> 2;
hereby assume F is formally_real;
   then QS F is negative-disjoint by lemma1;
   hence ex P being Subset of F st P is prepositive_cone;
   end;
assume ex P being Subset of F st P is prepositive_cone;
   then F is preordered;
   hence F is formally_real by AS,lemma3,lemma2;
end;
