h ^\ n is convergent_to_0

proof

A1: ( h is non-zero & h is convergent & lim h = 0. S ) by Def4;
hence h ^\ n is non-zero by Th17; :: according to NDIFF_1:def 4 :: thesis: ( h ^\ n is convergent & lim (h ^\ n) = 0. S )
thus ( h ^\ n is convergent & lim (h ^\ n) = 0. S ) by A1, LOPBAN_3:14; :: thesis: verum

end;

hence h ^\ n is convergent_to_0 ; :: thesis: verum