reserve D for non empty set,
  i,j,k for Nat,
  n,m for Nat,
  r for Real,
  e for real-valued FinSequence;

theorem Th27:
  for M1,M2 be Matrix of REAL st len M1 = len M2 holds SumAll M1 +
  SumAll M2 = SumAll(M1 ^^ M2)
proof
  let M1,M2 be Matrix of REAL such that
A1: len M1 = len M2;
  len Sum M1 = len M1 by Def1
    .= len Sum M2 by A1,Def1;
  then reconsider
  p1=Sum M1, p2 = Sum M2 as Element of (len Sum M1)-tuples_on REAL
  by FINSEQ_2:92;
  thus SumAll M1 + SumAll M2 = Sum (p1 + p2) by RVSUM_1:89
    .= SumAll(M1 ^^ M2) by Th26;
end;
