let O be set ; :: thesis: for G being GroupWithOperators of O
for H being StableSubgroup of G
for g1, g2 being Element of G st g1 in H & g2 in H holds
g1 * g2 in H
let G be GroupWithOperators of O; :: thesis: for H being StableSubgroup of G
for g1, g2 being Element of G st g1 in H & g2 in H holds
g1 * g2 in H
let H be StableSubgroup of G; :: thesis: for g1, g2 being Element of G st g1 in H & g2 in H holds
g1 * g2 in H
let g1, g2 be Element of G; :: thesis: ( g1 in H & g2 in H implies g1 * g2 in H )
assume A1: ( g1 in H & g2 in H ) ; :: thesis: g1 * g2 in H
H is Subgroup of G by Def7;
hence g1 * g2 in H by A1, GROUP_2:50; :: thesis: verum