theorem Th25:
  for S being non empty ManySortedSign holds
  S, S are_equivalent_wrt id the carrier of S, id the carrier' of S
proof
  let S be non empty ManySortedSign;
  set f = id the carrier of S, g = id the carrier' of S;
  thus f is one-to-one;
A1: f" = f by FUNCT_1:45;
  g" = g by FUNCT_1:45;
  hence thesis by A1,INSTALG1:8;
end;
