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

theorem
for f,g be PartFunc of REAL m,REAL, x0 be Element of REAL m
 st f is_continuous_in x0 & g is_continuous_in x0
 holds f+g is_continuous_in x0 & f-g is_continuous_in x0
proof
   let f,g be PartFunc of REAL m,REAL, x0 be Element of REAL m;
   assume f is_continuous_in x0 & g is_continuous_in x0; then
   <>*f is_continuous_in x0 & <>*g is_continuous_in x0 by Th37; then
A1:<>*f + <>*g is_continuous_in x0 & <>*f - <>*g is_continuous_in x0 by Th29;
   <>*f + <>*g = <>*(f+g) & <>*f - <>*g = <>*(f-g) by Th7;
   hence thesis by A1,Th37;
end;
