A1: h is convergent by Def4;
lim h = 0. S by Def4;
then A2: lim (h ^\ n) = 0. S by A1, LOPBAN_3:9;
h ^\ n is convergent by A1, LOPBAN_3:9;
hence for b₁ being sequence of S st b₁ = h ^\ n holds
b₁ is 0. S -convergent by A2; :: thesis: verum