theorem Th100:
  for X0 being non empty SubSpace of X st the carrier of X0 = 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 = A;
  then
  for x0 being Point of X0 holds ((modid(X,A))|X0) is_continuous_at x0 by Th98;
  hence thesis by Th44;
end;
