reserve m,n for non zero Element of NAT;
reserve i,j,k for Element of NAT;
reserve Z for set;

theorem
for f be PartFunc of REAL m,REAL, x0 be Element of REAL m, r be Real
 st f is_continuous_in x0 holds r(#)f is_continuous_in x0
proof
   let f be PartFunc of REAL m,REAL, x0 be Element of REAL m, r be Real;
   assume f is_continuous_in x0; then
A1:r(#)(<>*f) is_continuous_in x0 by Th30,Th37;
   r(#)(<>*f) = <>*(r(#)f) by Th8;
   hence thesis by A1,Th37;
end;
