reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th28:
  (X (\/) Y) (\/) Z = X (\/) (Y (\/) Z)
proof
    let i be object;
    assume
A1: i in I;
    hence (X (\/) Y (\/) Z).i = (X (\/) Y).i \/ Z.i by Def4
      .= X.i \/ Y.i \/ Z.i by A1,Def4
      .= X.i \/ (Y.i \/ Z.i) by XBOOLE_1:4
      .= X.i \/ (Y (\/) Z).i by A1,Def4
      .= (X (\/) (Y (\/) Z)).i by A1,Def4;
end;
