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 Th2:
  x0 in X & f is_continuous_in x0 implies f|X is_continuous_in x0
  proof
    assume that
A1: x0 in X and
A2: f is_continuous_in x0;
    consider g be PartFunc of REAL,REAL-NS n such that
A3: f=g & g is_continuous_in x0 by A2;
    g|X is_continuous_in x0 by A1,A3,NFCONT_3:6;
    hence thesis by A3;
  end;
