 reserve x,y,z for object,
   i,j,k,l,n,m for Nat,
   D,E for non empty set;
 reserve M for Matrix of D;
 reserve L for Matrix of E;

theorem EQ2:
  for i, j being Nat st M = L & [i,j] in Indices M
  holds M*(i,j) = L*(i,j)
  proof
    let i, j be Nat;
    assume AS1: M = L & [i,j] in Indices M; then
    consider p being FinSequence of D such that
    A1: p = M.i & M*(i,j) = p.j by MATRIX_0:def 5;
    consider q being FinSequence of E such that
    A2: q = L.i & L*(i,j) = q.j by MATRIX_0:def 5,AS1;
    thus M*(i,j) = L*(i,j) by AS1,A1,A2;
  end;
