reserve n,m,k for Element of NAT;
reserve x, X,X1,Z,Z1 for set;
reserve s,g,r,p,x0,x1,x2 for Real;
reserve s1,s2,q1 for Real_Sequence;
reserve Y for Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem
  f1|X is continuous & f2|X1 is continuous implies (f2*f1)|(X /\ (f1"X1)
  ) is continuous
proof
  (f2|X1)*(f1|X) = (f2*f1)|(X /\ (f1"X1)) by FUNCT_1:100;
  hence thesis;
end;
