let G be Group; :: thesis: for A being non empty Subset of G
for N being Subgroup of G holds N ` (N ` A) c= N ~ (N ~ A)
let A be non empty Subset of G; :: thesis: for N being Subgroup of G holds N ` (N ` A) c= N ~ (N ~ A)
let N be Subgroup of G; :: thesis: N ` (N ` A) c= N ~ (N ~ A)
N ` A c= N ~ A by Th18;
then N ` (N ` A) c= N ~ A by Th34;
hence N ` (N ` A) c= N ~ (N ~ A) by Th35; :: thesis: verum