reserve x, y for set;

theorem Th2:
  for C being set-id-inheriting carrier-underlaid category for a
  being Object of C holds idm a = id (a as_1-sorted)
proof
  let C be set-id-inheriting carrier-underlaid category;
  let a be Object of C;
  ex S being 1-sorted st a = S & the_carrier_of a = the carrier of S by Def3;
  then the_carrier_of a = the carrier of (a as_1-sorted) by Def1;
  hence thesis by YELLOW18:def 10;
end;
