chore(coinductive_predicates): remove private and use of import_private (#10084)
Remove a `private` modifier (I think this had previously been ported from core by @bryangingechen).
Then remove the only use of `import_private` from the library. (Besides another use in `tests/`, which we're not porting.)
(In mathlib4 we have `OpenPrivate` as an alternative. Removing `import_private` is one less thing for mathport to care about.)
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>