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
  for R being Tolerance of X holds for x st x in X holds
  ex y st x in Class(R,y)
proof
  let R be Tolerance of X;
  let x;
  assume x in X;
  then x in Class(R,x) by Th20;
  hence thesis;
end;
