[isabelle] Nominal2 fails on Datatypes with Lists

Hello All,

I have been recently experimenting with Nominal2<https://www.isa-afp.org/entries/Nominal2.html>, but have run into a problem with lists in datatypes.

The datatype

nominal_datatype ty

  = TRecord ‹ty list›

  | TVar typevar

fails with

Proof failed.

 1. ⋀x. TRecord_raw (map (permute p_) (- p_ ∙ x)) = TRecord_raw x

The error(s) above occurred for the goal statement⌂:

p_ ∙ TRecord_raw = TRecord_raw

presumably because the automation does not know (or use) the fact that ‹map (permute p) xs = p ∙ xs›.
Further, although I can prove the lemma, I am unsure how (or if it is possible) to 'inject' the fact into the automation.

Any advice on how to proceed would be appreciated.

Thank you,
Vincent Jackson

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