
theorem LmSign1EX:
  for n, i, j 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
  holds Delete(M,i,j) is Matrix of n, F_Rat
  proof
    let n, i, j 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;
    reconsider L = M as Matrix of n+1, F_Rat by A2;
    X1: Delete(M,i,j) = Delete(L,i,j) by LmSign1E,A1,A3;
    (n+1)-'1 = n by NAT_D:34;
    hence thesis by X1;
  end;
