Various improvements to `Permutation` lemmas and instances
Various changes to Permutation lemmas:
- Rename
Permutation_nil→Permutation_nil_rand andPermutation_singleton→Permutation_singleton_r. - Add lemmas
Permutation_nil_landPermutation_singleton_l. - Add new instance
cons_Permutation_inj_l : Inj (=) (≡ₚ) (.:: k).. - Add lemma
Permutation_cross_split. - Make lemma
elem_of_Permutationa biimplication
Also, I made the following changes that should not affect users:
- Name
ProperandInjinstances forPermutationasoperation_Permutation_{Proper,inj,inj_l,inj_r} - Remove
Properinstances for::and++that are already supplied by the std lib.
Edited by Robbert Krebbers