reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;
reserve
  A0 for (X,S)-terms non-empty MSAlgebra over S,
  A1 for all_vars_including (X,S)-terms MSAlgebra over S,
  A2 for all_vars_including inheriting_operations (X,S)-terms MSAlgebra over S,
  A for all_vars_including inheriting_operations free_in_itself
  (X,S)-terms MSAlgebra over S;
reserve X0 for non-empty countable ManySortedSet of S;
reserve A0 for all_vars_including inheriting_operations free_in_itself
  (X0,S)-terms MSAlgebra over S;

theorem Th77:
  for I being set
  for A being ManySortedSet of I
  ex R being ManySortedRelation of A
  st R = I-->{} & R is terminating
  proof
    let I be set;
    let A be ManySortedSet of I;
    set R = I-->{};
    for i being set st i in I holds R.i is Relation of A.i by XBOOLE_1:2;
    then reconsider R as ManySortedRelation of A by MSUALG_4:def 1;
    take R;
    thus R = I-->{};
    let i be set;
    thus thesis;
  end;
