reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;
reserve O for connected non empty Poset;
reserve R,Q for array of O;

theorem Th59:
  c in (succ b)\a iff a c= c & c c= b
  proof
    a c= c iff c nin a by ORDINAL6:4; then
    c in (succ b)\a iff c in succ b & a c= c by XBOOLE_0:def 5;
    hence thesis by ORDINAL1:22;
  end;
