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:];

theorem
  id X is_reflexive_in X & id X is_symmetric_in X & id X is_transitive_in X
    by RELAT_1:def 10;
