
theorem oext2:
for F being ordered polynomial_disjoint Field,
    P being Ordering of F
for a being non square Element of F
holds P extends_to FAdj(F,{sqrt a}) iff a in P
proof
let F be ordered polynomial_disjoint Field, P be Ordering of F;
let a be non square Element of F;
set b = sqrt a;
H: b^2 = a by FIELD_9:53; then
b^2 in F;
hence thesis by H,oext1;
end;
