
theorem FAutEQ:
for F being Field
for E1,E2 being FieldExtension of F st E1 == E2
holds the set of all f where f is Automorphism of E1
    = the set of all f where f is Automorphism of E2
proof
let F be Field, E1,E2 being FieldExtension of F;
assume AS: E1 == E2;
A: now let o be object;
   assume o in the set of all f where f is Automorphism of E1; then
   consider g being Automorphism of E1 such that B: o = g;
   g is Automorphism of E2 by AS,FAutEQ1;
   hence o in the set of all f where f is Automorphism of E2 by B;
   end;
now let o be object;
   assume o in the set of all f where f is Automorphism of E2; then
   consider g being Automorphism of E2 such that B: o = g;
   g is Automorphism of E1 by AS,FAutEQ1;
   hence o in the set of all f where f is Automorphism of E1 by B;
   end;
hence thesis by A,TARSKI:2;
end;
