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 X overlaps Y & X overlaps Z
proof
  assume X overlaps Y (/\) Z;
  then consider x such that
A1: x in X and
A2: x in Y (/\) Z by Th11;
  x in Y & x in Z by A2,Th8;
  hence thesis by A1,Th10;
end;
