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
  A0 is Equations(S,A0)-free
  proof
    reconsider G = FreeGen X0 as GeneratorSet of A0 by Th45;
    take G; thus thesis by Th75;
  end;
