reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem Th1:
  for A being reflexive non empty RelStr, a being Element of A holds a <= a
proof
  let A be reflexive non empty RelStr, a be Element of A;
  the InternalRel of A is_reflexive_in the carrier of A by Def2;
  then [a,a] in the InternalRel of A;
  hence thesis;
end;
