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 b_{1} being sequence of S st b_{1} = h ^\ n holds

b_{1} is 0. S -convergent
by A2; :: thesis: verum

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 b

b