theorem
  f1|X is Lipschitzian & f2|X1 is Lipschitzian implies (f1-f2)|(X /\ X1)
  is Lipschitzian
proof
A1: f1|(X /\ X1) = f1|X|(X /\ X1) & f2|(X /\ X1) = f2|X1|(X /\ X1) by
RELAT_1:74,XBOOLE_1:17;
A2: (f1-f2)|(X /\ X1) = f1|(X /\ X1)-f2|(X /\ X1) by RFUNCT_1:47;
  assume f1|X is Lipschitzian & f2|X1 is Lipschitzian;
  hence thesis by A1,A2;
end;
