reserve I for set;

theorem
  for A being ManySortedSet of I holds (id A)""A = A
proof
  let A be ManySortedSet of I;
A1: rngs (id A) = A by EXTENS_1:9;
  doms (id A) = A by MSSUBFAM:17;
  hence thesis by A1,Th14;
end;
