reserve n,m,i,k for Element of NAT;
reserve x,X,X1 for set;
reserve r,p for Real;
reserve s,x0,x1,x2 for Real;
reserve f,f1,f2 for PartFunc of REAL,REAL n;
reserve h for PartFunc of REAL,REAL-NS n;
reserve W for non empty set;

theorem
 for f be PartFunc of REAL n,REAL,
     h be PartFunc of REAL-NS n,REAL,
     x0 be Element of REAL n,
     y0 be Point of REAL-NS n
  st f=h & x0=y0 holds
  f is_continuous_in x0 iff h is_continuous_in y0;
