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

theorem Th62:
  X (/\) (Y (\) Z) = (X (/\) Y) (\) Z
proof
    let i be object;
    assume
A1: i in I;
    hence (X (/\) (Y (\) Z)).i = X.i /\ (Y (\) Z).i by Def5
      .= X.i /\ (Y.i \ Z.i) by A1,Def6
      .= X.i /\ Y.i \ Z.i by XBOOLE_1:49
      .= (X (/\) Y).i \ Z.i by A1,Def5
      .= ((X (/\) Y) (\) Z).i by A1,Def6;
end;
