reserve
F for non 2-characteristic non quadratic_complete polynomial_disjoint Field;

theorem
for a being non square Element of F
holds the carrier of FAdj(F,{sqrt a}) =
      the set of all y + @(sqrt a) * z
                      where y,z is F-membered Element of FAdj(F,{sqrt a})
proof
let a be non square Element of F;
A: now let o be object;
   assume o in the carrier of FAdj(F,{sqrt a});
   then ex y,z being F-membered Element of FAdj(F,{sqrt a})
              st o = y + @(sqrt a) * z by qbase2;
   hence o in the set of all y + @(sqrt a) * z
                    where y,z is F-membered Element of FAdj(F,{sqrt a});
   end;
now let o be object;
  assume o in the set of all y + @(sqrt a) * z
                    where y,z is F-membered Element of FAdj(F,{sqrt a});
  then ex y,z being F-membered Element of FAdj(F,{sqrt a})
              st o = y + @(sqrt a) * z;
  hence o in the carrier of FAdj(F,{sqrt a});
  end;
hence thesis by A,TARSKI:2;
end;
