reserve i for Nat, x,y for set;
reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;

theorem
  for S1,S2 being ManySortedSign
  st the ManySortedSign of S1 = the ManySortedSign of S2
  for o,a be set, r1 be Element of S1 for r2 being Element of S2 st r1 = r2
  holds o is_of_type a,r1 implies o is_of_type a,r2;
