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 Th42:
  SumAll MR = Sum Mx2FinS MR
proof
  per cases;
  suppose
A1: len MR = 0;
    hence Sum Mx2FinS MR = 0 by Def5,RVSUM_1:72
      .= SumAll MR by A1,MATRPROB:23;
  end;
  suppose
    len MR > 0;
    then
    ex p being FinSequence of REAL* st Mx2FinS(MR) = p.(len MR) & len p
= len MR & p.1 = MR.1 & for k st k >= 1 & k < len MR holds p.(k+ 1) = (p.k) ^
    MR.(k+1) by Def5;
    hence thesis by Th38;
  end;
end;
