let G be Group; :: thesis: for f being Element of Aut G holds
( dom f = rng f & dom f = the carrier of G )
let f be Element of Aut G; :: thesis: ( dom f = rng f & dom f = the carrier of G )
reconsider f = f as Homomorphism of G,G by Def1;
A1: f is bijective by Th4;
then dom f = the carrier of G by GROUP_6:61;
hence ( dom f = rng f & dom f = the carrier of G ) by A1, GROUP_6:61; :: thesis: verum