
theorem po2:
for F being Field, E being FieldExtension of F
for L being F-monomorphic Field,
    f being Monomorphism of F,L
for p,q being Element of Ext_Set(f,E) st p <= q & q <= p holds p = q
proof
let F be Field, E being FieldExtension of F;
let L be F-monomorphic Field;
let f be Monomorphism of F,L , p,q be Element of Ext_Set(f,E);
assume AS: p <= q & q <= p;
consider K1 being FieldExtension of p`1, g1 being Function of K1,L such that
B: K1 = q`1 & g1 = q`2 & g1 is (p`2)-extending by AS;
E: p`1 is Subfield of q`1 & q`1 is Subfield of p`1 by AS,FIELD_4:7;
   p`2 = q`2 by B,E,EC_PF_1:4;
hence thesis by E,EC_PF_1:4,XTUPLE_0:2;
end;
