
theorem
  for n, i, j, k, m being Nat, M being Matrix of n+1, F_Real
  st 0 < n & M is Matrix of n+1, F_Rat &
  [i, j] in Indices M & [k, m] in Indices (Delete(M,i,j))
  holds (Delete(M,i,j))*(k,m) is Element of F_Rat
  proof
    let n, i, j, k, m be Nat, M be Matrix of n+1,F_Real;
    assume that
    A1: 0 < n and
    A2: M is Matrix of n+1, F_Rat and
    A3: [i, j] in Indices M and
    A4: [k, m] in Indices (Delete(M,i,j));
    reconsider L = M as Matrix of n+1, F_Rat by A2;
    (Delete(M,i,j))*(k,m) = (Delete(L,i,j))*(k,m)
    by LmSign1F,A1,A3,A4;
    hence thesis;
  end;
