
theorem XX:
for F being Field,
    p being non constant Element of the carrier of Polynom-Ring F
for E being SplittingField of p 
holds E == FAdj(F,Roots(E,p))
proof
let F be Field,
    p be non constant Element of the carrier of Polynom-Ring F;
let E be SplittingField of p;
set K = FAdj(F,Roots(E,p));
p splits_in E by defspl; then
K is SplittingField of p by spl1; then
p splits_in K by defspl;
hence thesis by defspl;
end;
