Hi,

suppose I have a function (f :num -> num -> real), and I want to calculate the 
sum of (f i j) on the entire plane, one way is to use double suminf: (assuming 
it is always summable, i.e. any sum is finite)

  suminf (λi. suminf (λj. f i j)))                                      (1)

However, there’s another way using single suminf, based on numpairTheory:

  suminf (λn. f (nfst n) (nsnd n))                              (2)

My question is: how can I prove (1) and (2) are equal, i.e.:

  suminf (λi. suminf (λj. f i j))) = suminf (λn. f (nfst n) (nsnd n))

?

--Chun

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