
theorem LM36:
  for F,G be FinSequence of REAL
  st dom F = dom G
   & ( for i being Element of dom F holds G.i = (F.i)" )
  holds Product G = (Product F)"
  proof
    let F,G be FinSequence of REAL;
    assume that
    A1: dom F = dom G and
    A2: for i being Element of dom F holds G.i = (F.i)";
    A3: len F = len G by A1,FINSEQ_3:29;
    for i being Element of NAT st i in dom F holds G.i = (F.i)" by A2;
    hence thesis by A3,LM36A;
  end;
