h ^\ n is convergent_to_0

proof

A1: ( h is non-zero & h is convergent & lim h = 0 ) by Def1;
thus h ^\ n is non-zero ; :: according to CFDIFF_1:def 1 :: thesis: ( h ^\ n is convergent & lim (h ^\ n) = 0 )
thus ( h ^\ n is convergent & lim (h ^\ n) = 0 ) by A1, CFCONT_1:43; :: thesis: verum

end;

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