reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th38:
  for A being included_in_Seg set holds dom Sgm A = Seg card A
  proof
    let A be included_in_Seg set;
    len Sgm A = card A by Th37;
    hence thesis by FINSEQ_1:def 3;
  end;
