theorem Th17:
  Len (F1|n) = (Len F1) |n
proof
A1: len Len F1=len F1 by CARD_1:def 7;
  per cases;
  suppose
A2: n>=len F1;
    then F1|n=F1 by FINSEQ_1:58;
    hence thesis by A1,A2,FINSEQ_1:58;
  end;
  suppose
A3: n<len F1;
    F1=(F1|n)^(F1/^n) by RFINSEQ:8;
    then
A4: Len F1=(Len (F1|n))^Len (F1/^n) by Th14;
    len (F1|n) =n by A3,FINSEQ_1:59;
    then len Len (F1|n)=n by CARD_1:def 7;
    hence thesis by A4,FINSEQ_5:23;
  end;
end;
