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

theorem Th29:
for f,g be PartFunc of REAL m,REAL n, x be Element of REAL m
 st f is_continuous_in x & g is_continuous_in x
 holds f+g is_continuous_in x & f-g is_continuous_in x
proof
   let f,g be PartFunc of REAL m,REAL n,
       x be Element of REAL m;
   assume A1: f is_continuous_in x & g is_continuous_in x;
   reconsider y=x as Point of REAL-NS m by REAL_NS1:def 4;
A2:the carrier of REAL-NS m = REAL m &
   the carrier of REAL-NS n = REAL n by REAL_NS1:def 4; then
   reconsider f1=f, g1=g as PartFunc of REAL-NS m, REAL-NS n;
A3:f1+g1 is_continuous_in y & f1-g1 is_continuous_in y by NFCONT_1:15,A1;
   f+g=f1+g1 & f-g=f1-g1 by A2,NFCONT_4:5,10;
   hence thesis by A3;
end;
