let G be addGroup; :: thesis: for a being Element of G
for A being Subset of G
for H being Subgroup of G holds (H + a) + A = H + (a + A)
let a be Element of G; :: thesis: for A being Subset of G
for H being Subgroup of G holds (H + a) + A = H + (a + A)
let A be Subset of G; :: thesis: for H being Subgroup of G holds (H + a) + A = H + (a + A)
let H be Subgroup of G; :: thesis: (H + a) + A = H + (a + A)
thus (H + a) + A = (H + {a}) + A
.= H + (a + A) by Th98 ; :: thesis: verum