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

theorem
  X overlaps Y (\) Z implies Y overlaps X (\) Z
proof
  assume
A1: X overlaps Y (\) Z;
  let i be object;
  assume
A2: i in I;
  then X.i meets (Y (\) Z).i by A1;
  then X.i meets Y.i \ Z.i by A2,Def6;
  then Y.i meets X.i \ Z.i by XBOOLE_1:81;
  hence thesis by A2,Def6;
end;
