reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem Th23:
  for p,q being FinSequence st p^q is Function-yielding holds p is
  Function-yielding & q is Function-yielding
proof
  let p,q be FinSequence;
  assume
A1: for x being object st x in dom (p^q) holds (p^q).x is Function;
  hereby
    let x be object;
    assume
A2: x in dom p;
    then (p^q).x = p.x by FINSEQ_1:def 7;
    hence p.x is Function by A1,A2,FINSEQ_3:22;
  end;
  let x be object;
  assume
A3: x in dom q;
  then reconsider i = x as Nat;
  (p^q).(len p+i) = q.x by A3,FINSEQ_1:def 7;
  hence thesis by A1,A3,FINSEQ_1:28;
end;
