[isabelle] Summing/subtracting functions



Hi,

Is the summation (and/or subtraction) of functions already defined in the
library?

axiomatization
f :: "nat => nat" and
g :: "nat => nat" where
ax1 : "ALL x. f x = 2" and
ax2 : "ALL x. g x = 1"

lemma "f - g = g"
using ax1 ax2
apply auto

Presuming it's not, why not? It seems that there's only one definition for
summation/subtraction of functions anyway, i.e. "f - g <--> ALL x. f x - g
x" -- is it not?

Thanks

Steve




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