reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;

theorem Th24:
  for f be Sequence holds
  base-f = 0 & limit-f = dom f & len-f = dom f
  proof
    let f be Sequence;
    per cases;
    suppose f = {};
      hence thesis by Th15;
    end;
    suppose
A1:   f <> {};
      (dom f)\0 = dom f;
      hence base-f = 0 & limit-f = dom f by A1,Th23;
      hence len-f = dom f by ORDINAL3:56;
    end;
  end;
