let O be set ; :: thesis: for G being GroupWithOperators of O holds G is StableSubgroup of G
let G be GroupWithOperators of O; :: thesis: G is StableSubgroup of G
A1: for o being Element of O holds G ^ o = (G ^ o) | the carrier of G ;
G is Subgroup of G by GROUP_2:54;
hence G is StableSubgroup of G by A1, Def7; :: thesis: verum