theorem Th117:
  for a being Real, x being real-valued FinSequence
   holds len (a*x)=len x
proof
  let a be Real, x be real-valued FinSequence;
  set n=len x;
  x is FinSequence of REAL by Lm2;
  then reconsider z=x as Element of n-tuples_on REAL by FINSEQ_2:92;
  len (a*z)=n by CARD_1:def 7;
  hence thesis;
end;
