A further remark:

>     1.17 +definition ntrancl :: "('a * 'a => bool) => nat => ('a * 'a => 
> bool)"
>     1.18 +where
>     1.19 + [code del]: "ntrancl R n = (UN i : {i. 0 < i & i <= (Suc n)}. R ^^ 
> i)"

Canonically and keeping in mind the upcoming 'a set, this would be

definition ntrancl :: "nat => ('a * 'a) set => ('a * 'a) set"

        Florian

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