
theorem Fsuba:
for F being Field, E being FieldExtension of F,
    L be F-monomorphic Field
for f being Monomorphism of F,L
for S being ascending non empty Subset of Ext_Set(f,E)
holds F is Subfield of unionField(S,f,E)
proof
let F be Field, E be FieldExtension of F;
let L be F-monomorphic Field;
let f be Monomorphism of F,L;
let S be ascending non empty Subset of Ext_Set(f,E);
set p = the Element of S;
A2: F is Subfield of p`1 by FIELD_4:7;
p`1 is Subfield of unionField(S,f,E) by Fsubb;
hence thesis by A2,EC_PF_1:5;
end;
