theorem Th99:
  for X0 being non empty SubSpace of X st the carrier of X0
  misses A holds (modid(X,A))|X0 is continuous Function of X0,X
  modified_with_respect_to A
proof
  let X0 be non empty SubSpace of X;
  assume (the carrier of X0) misses A;
  then
  for x0 being Point of X0 holds ((modid(X,A))|X0) is_continuous_at x0 by Th97;
  hence thesis by Th44;
end;
