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 Th20: :: FINSEQ_3:44
  for A being finite natural-membered set holds len(Sgm0 A) = card A
proof
  let A be finite natural-membered set;
  rng(Sgm0 A) = A by Def4;
  then (len(Sgm0 A)),A are_equipotent by WELLORD2:def 4;
  then card A = card((len(Sgm0 A))) by CARD_1:5;
  hence thesis;
end;
