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

theorem Th29:
  (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 Def5
      .= X.i /\ Y.i /\ Z.i by A1,Def5
      .= X.i /\ (Y.i /\ Z.i) by XBOOLE_1:16
      .= X.i /\ (Y (/\) Z).i by A1,Def5
      .= (X (/\) (Y (/\) Z)).i by A1,Def5;
end;
