reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;

theorem Th5:
  for R being total reflexive Relation of X holds x in X implies [x,x] in R
proof
  let R be total reflexive Relation of X;
  field R = X by ORDERS_1:12;
  then R is_reflexive_in X by RELAT_2:def 9;
  hence thesis;
end;
