theorem Threcursive02:
  ex f being set st f in ConFuncs(FlatPoset(X),FlatPoset(Y)) &
     f = RecFunc01(f,E,I,J,D)
  proof
    set FX = FlatPoset(X);
    set FY = FlatPoset(Y);
    set FlatC = FlatConF(X,Y);
    set CFXY = ConFuncs(FX,FY);
    set CRFXY = ConRelat(FX,FY);
    consider W be continuous Function of FlatC,FlatC such that
A4: for f being Element of CFXY
       holds W.f = RecFunc01(f,E,I,J,D) by Threcursive01;
    reconsider W as monotone Function of FlatC,FlatC;
    reconsider f = least_fix_point(W) as Element of FlatC;
A5: f is_a_fixpoint_of W by POSET_1:def 5;
A6: f = W.f by A5,ABIAN:def 3;
    take f;
    thus thesis by A4,A6;
  end;
