let G be addGroup; :: thesis: for a being Element of G
for A being Subset of G
for H being Subgroup of G holds (A + a) + H = A + (a + H)
let a be Element of G; :: thesis: for A being Subset of G
for H being Subgroup of G holds (A + a) + H = A + (a + H)
let A be Subset of G; :: thesis: for H being Subgroup of G holds (A + a) + H = A + (a + H)
let H be Subgroup of G; :: thesis: (A + a) + H = A + (a + H)
thus (A + a) + H = A + ({a} + H) by Th96
.= A + (a + H) ; :: thesis: verum