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,PC being a_partition of Y st
  PA '>' PC & PB '>' PC holds PA '/\' PB '>' PC
proof
  let PA,PB,PC be a_partition of Y;
  assume PA '>' PC & PB '>' PC;
then A1: ERl(PC) c= ERl(PA) & ERl(PC) c= ERl(PB) by Th20;
 ERl(PA '/\' PB) = ERl(PA) /\ ERl(PB) by Th24;
then  ERl(PC) c= ERl(PA '/\' PB) by A1,XBOOLE_1:19;
  hence thesis by Th20;
end;
