
theorem for f1,f2 being FinSequence of REAL st len f1 = len f2 & (for k
  being Element of NAT st k in dom f1 holds f1.k>=f2.k & f2.k>0) holds
  Product f1 >= Product f2
proof
  let f1,f2 be FinSequence of REAL such that
  A1: len f1 = len f2 & (for k
  being Element of NAT st k in dom f1 holds f1.k>=f2.k & f2.k>0);
  for k be Element of NAT st k in dom f2 holds f1.k>=f2.k & f2.k>0
  proof
    let k be Element of NAT such that
    B1: k in dom f2;
    k in dom f1 by A1,B1,FINSEQ_3:29;
    hence thesis by A1;
  end;
hence thesis by A1,NAT_4:54;
end;
