
theorem Th9:
  for p being FinSequence, n being Nat st n in dom p & n+1 <= len p
  holds mid(p,n,n+1) = <*p.n, p.(n+1)*>
proof
  let p be FinSequence, n be Nat;
  assume A1: n in dom p & n+1 <= len p;
  then n+1 in dom p by FINSEQ_3:25, XREAL_1:31;
  then A2: mid(p,n+1,n+1) = <*p.(n+1)*> by Th7;
  thus mid(p,n,n+1) = <*p.n*> ^ mid(p,n+1,n+1) by A1, Th8, XREAL_1:29
    .= <*p.n, p.(n+1)*> by A2, FINSEQ_1:def 9;
end;
