let G be Group; :: thesis: for a being Element of G
for H1, H2 being Subgroup of G holds (H1 * H2) * a = H1 * (H2 * a)
let a be Element of G; :: thesis: for H1, H2 being Subgroup of G holds (H1 * H2) * a = H1 * (H2 * a)
let H1, H2 be Subgroup of G; :: thesis: (H1 * H2) * a = H1 * (H2 * a)
thus (H1 * H2) * a = (H1 * (carr H2)) * a
.= H1 * (H2 * a) by GROUP_2:98 ; :: thesis: verum