reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th37:
  for M being Matrix of REAL for p being FinSequence of REAL* st (
for k st k >= 1 & k < len M holds p.(k+1)=(p.k) ^ M.(k+1)) holds for k st k >=
  1 & k < len M holds Sum(p.(k+1))=Sum(p.k)+Sum(M.(k+1))
proof
  let M be Matrix of REAL;
  let p be FinSequence of REAL* such that
A1: for k st k >= 1 & k < len M holds p.(k+1) = (p.k) ^ M.(k+1);
  let k such that
A2: k >= 1 and
A3: k < len M;
  p.(k+1) = (p.k) ^ M.(k+1) by A1,A2,A3;
  hence thesis by RVSUM_1:75;
end;
