reserve i,j,m,n,k for Nat,
  x,y for set,
  K for Field,
  a for Element of K;

theorem Th3:
  for A,B be Matrix of K for P, Q be without_zero finite Subset of NAT
  st [:P,Q:] c= Indices A holds Segm(A+B,P,Q) = Segm(A,P,Q) + Segm(B,P,Q)
proof
  let A,B be Matrix of K;
  let P, Q be without_zero finite Subset of NAT;
  rng (Sgm Q)=Q & rng (Sgm P)=P by FINSEQ_1:def 14;
  hence thesis by Th1;
end;
