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
 st f is_continuous_in x0 holds |.f.| is_continuous_in x0
proof
   let f be PartFunc of REAL m,REAL, x0 be Element of REAL m;
   assume f is_continuous_in x0; then
   <>*f is_continuous_in x0 by Th37; then
   |. <>*f .| is_continuous_in x0 by Th32;
   hence thesis by Th9;
end;
