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;

theorem
  x-tree {} = root-tree x
  proof
    dom(x-tree {}) = elementary_tree 0 by TREES_4:10,FUNCT_6:23,TREES_3:52;
    hence x-tree {} = root-tree ((x-tree {}).{}) by TREES_4:5
    .= root-tree x by TREES_4:def 4;
  end;
