reserve x, y for set;

theorem
  for C being carrier-underlaid category, a being Object of C holds
  the_carrier_of a = the carrier of a as_1-sorted
proof
  let C be carrier-underlaid category, a be Object of C;
  ex S being 1-sorted st a = S & the_carrier_of a = the carrier of S by Def3;
  hence thesis by Def1;
end;
