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

theorem Th99:
  X overlaps Y & Y c= Z implies X overlaps Z
proof
  assume that
A1: X overlaps Y and
A2: Y c= Z;
  consider x such that
A3: x in X and
A4: x in Y by A1,Th11;
  x in Z by A2,A4,Th9;
  hence thesis by A3,Th10;
end;
