
theorem Th44:
  for S being non empty ManySortedSign holds S is unsplit iff for
  o being object st o in the carrier' of S holds (the ResultSort of S).o = o
proof
  let S be non empty ManySortedSign;
  thus S is unsplit implies
  for o being object st o in the carrier' of S holds
  (the ResultSort of S).o = o by FUNCT_1:17;
  assume
A1: for o being object st o in the carrier' of S holds (the ResultSort of S
  ).o = o;
  dom the ResultSort of S = the carrier' of S by FUNCT_2:def 1;
  hence the ResultSort of S = id the carrier' of S by A1,FUNCT_1:17;
end;
