reserve Y,Z for non empty set;
reserve PA,PB for a_partition of Y;
reserve A,B for Subset of Y;
reserve i,j,k for Nat;
reserve x,y,z,x1,x2,y1,z0,X,V,a,b,d,t,SFX,SFY for set;

theorem
  for PA,PB being a_partition of Y st
  x in (PA '\/' PB) & z0 in PA & t in x & t in z0 holds z0 c= x by Th16,Th18;
