theorem LemP:
  for p,q being FinSequence st i <= len p holds (p^q)|Seg i = p|Seg i
  proof
    let p,q be FinSequence;
    set D = (rng p)\/(rng q)\/{0};
    rng p c= (rng p)\/rng q & rng q c= (rng p)\/rng q by XBOOLE_1:7;
    then p is FinSequence of D & q is FinSequence of D & (p^q)|i = (p^q)|Seg i
    & p|Seg i = p|i by FINSEQ_1:def 4,XBOOLE_1:10;
    hence thesis by FINSEQ_5:22;
  end;
