
theorem
for F being ordered polynomial_disjoint Field
for a being non square Element of F
st a in QS F holds FAdj(F,{sqrt a}) is formally_real
proof
let F be ordered polynomial_disjoint Field, a be non square Element of F;
assume A: a in QS F;
(sqrt a)^2 = a by FIELD_9:53;
hence thesis by A,FF1;
end;
