reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th50:
  for p being nonnegative FinSequence of REAL st r1>=0 & r2>=0
holds for i st i in dom p & p.i = r1*r2 holds (Infor_FinSeq_of p).i = r1*r2*log
  (2,r1) + r1*r2*log(2,r2)
proof
  let p be nonnegative FinSequence of REAL such that
A1: r1>=0 and
A2: r2>=0;
  let i such that
A3: i in dom p and
A4: p.i = r1*r2;
  len p = len Infor_FinSeq_of p by Th47;
  then i in dom Infor_FinSeq_of p by A3,FINSEQ_3:29;
  hence (Infor_FinSeq_of p).i = r1*r2*log(2,r1*r2) by A4,Th47
    .= r1*r2*log(2,r1) + r1*r2*log(2,r2) by A1,A2,Th6;
end;
