
theorem
for f1,f2 be without+infty Function of [:NAT,NAT:],ExtREAL holds
  Partial_Sums(f1 + f2) = Partial_Sums f1 + Partial_Sums f2
proof
   let f1,f2 be without+infty Function of [:NAT,NAT:],ExtREAL;
   Partial_Sums(f1+f2)
    = Partial_Sums_in_cod2(Partial_Sums_in_cod1 f1 +Partial_Sums_in_cod1 f2)
      by Th45;
   hence thesis by Th45;
end;
