let G be Group; :: thesis: for a being Element of G
for A being Subset of G
for H being Subgroup of G holds (A * H) * a = A * (H * a)
let a be Element of G; :: thesis: for A being Subset of G
for H being Subgroup of G holds (A * H) * a = A * (H * a)
let A be Subset of G; :: thesis: for H being Subgroup of G holds (A * H) * a = A * (H * a)
let H be Subgroup of G; :: thesis: (A * H) * a = A * (H * a)
thus (A * H) * a = A * (H * {a}) by GROUP_2:97
.= A * (H * a) ; :: thesis: verum