reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;

theorem Th22:
  (Sgm0 {n}).0=n
proof
  len (Sgm0 {n})=card {n} by Th20;
  then 0 in dom (Sgm0 {n}) by AFINSQ_1:86;
  then
A1: (Sgm0 {n}).0 in rng (Sgm0 {n}) by FUNCT_1:def 3;
  rng (Sgm0 {n})={n} by Def4;
  hence thesis by A1,TARSKI:def 1;
end;
