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 holds PA '\/' (PA '/\' PB) = PA
proof
  let PA,PB be a_partition of Y;
   ERl
(PA '\/' (PA '/\' PB)) = ERl(PA) "\/" ERl(PA '/\' PB) & ERl(PA) "\/" ERl(
  PA '/\' PB) = ERl(PA) "\/" (ERl(PA) /\ ERl(PB)) by Th23,Th24;
  hence thesis by Th25,EQREL_1:17;
end;
