reserve a,b,i,j,k,l,m,n for Nat;

theorem ::POLYNOM4:1
  for f be complex-valued FinSequence holds
    f = (f|i)^((f/^i)|(1 qua Nat))^(f/^(i+1))
  proof
    let f be complex-valued FinSequence;
    f = (f|i)^(f/^i) by RFINSEQ:8
    .= (f|i)^(((f/^i)| 1)^((f/^i)/^1)) by RFINSEQ:8
    .= (f|i)^((f/^i)| 1)^((f/^i)/^1) by FINSEQ_1:32
    .= (f|i)^((f/^i)| 1)^(f/^(i+1)) by FINSEQ681;
    hence thesis;
  end;
