let O be set ; :: thesis: for G being GroupWithOperators of O
for H being StableSubgroup of G
for g being Element of G st g in H holds
g " in H
let G be GroupWithOperators of O; :: thesis: for H being StableSubgroup of G
for g being Element of G st g in H holds
g " in H
let H be StableSubgroup of G; :: thesis: for g being Element of G st g in H holds
g " in H
let g be Element of G; :: thesis: ( g in H implies g " in H )
assume A1: g in H ; :: thesis: g " in H
H is Subgroup of G by Def7;
hence g " in H by A1, GROUP_2:51; :: thesis: verum