
theorem Th64:
for f be nonnegative Function of [:NAT,NAT:],ExtREAL, n be Element of NAT
 holds ProjMap2(Partial_Sums_in_cod1 f,n) is non-decreasing
proof
   let f be nonnegative without-infty Function of [:NAT,NAT:],ExtREAL,
       n be Element of NAT;
A1:ProjMap1(Partial_Sums_in_cod2 ~f,n) is non-decreasing by Th63;
   Partial_Sums_in_cod2 ~f = ~Partial_Sums_in_cod1 f by Th40;
   hence ProjMap2(Partial_Sums_in_cod1 f,n) is non-decreasing by A1,Th33;
end;
