
theorem lem1a:
for F being Field, E being FieldExtension of F,
    L being F-monomorphic Field
for f being Monomorphism of F,L,
    S being non empty Subset of Ext_Set(f,E)
for p,q being Element of S
for a being Element of p`1 holds p <= q implies a in the carrier of q`1
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 non empty Subset of Ext_Set(f,E);
let p,q be Element of S, a be Element of p`1;
assume p <= q; then
p`1 is Subfield of q`1 by FIELD_4:7; then
the carrier of p`1 c= the carrier of q`1 by EC_PF_1:def 1;
hence thesis;
end;
