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;

theorem
  for X st X is included_in_Seg holds Sgm X = {} iff X = {}
proof
  let X;
  assume X is included_in_Seg;
  then rng Sgm X = X by Def13;
  hence thesis;
end;
