reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;
reserve a, b, c, d, e, f for object;
reserve x1,x2,y1,y2 for object;

theorem
  for q being FinSubsequence holds dom Seq q = dom Sgm dom q
proof
  let q be FinSubsequence;
  rng Sgm dom q = dom q by Th50;
  hence thesis by RELAT_1:27;
end;
