let h be Function of T,(TOP-REAL n); :: thesis: ( h = f [+] r implies h is continuous )
assume A1: h = f [+] r ; :: thesis: h is continuous
reconsider r = r as Element of R^1 by XREAL_0:def 1;
dom f = the carrier of T by FUNCT_2:def 1;
then h = f <+> (T --> r) by A1, Th29;
hence h is continuous ; :: thesis: verum