 reserve X, Y for set, A for Ordinal;

theorem Th1:
  X c= Y implies succRel(X) c= succRel(Y)
proof
  assume A1: X c= Y;
  now
    let x,y be object;
    reconsider a=x,b=y as set by TARSKI:1;
    assume [x,y] in succRel(X);
    then [a,b] in succRel(X);
    then a in X & b in X & b = succ a by Def1;
    hence [x,y] in succRel(Y) by A1, Def1;
  end;
  hence thesis by RELAT_1:def 3;
end;
