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 Th25:
  for PA,PB being a_partition of Y st ERl(PA) = ERl(PB) holds PA = PB
proof
  let PA,PB be a_partition of Y;
  assume ERl(PA)=ERl(PB);
then  PA '<' PB & PB '<' PA by Th20;
  hence thesis by Th4;
end;
