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

theorem Th73:
  (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 Def6
      .= X.i \ Y.i \ Z.i by A1,Def6
      .= X.i \ (Y.i \/ Z.i) by XBOOLE_1:41
      .= X.i \ (Y (\/) Z).i by A1,Def4
      .= (X (\) (Y (\/) Z)).i by A1,Def6;
end;
