(* We can't declare a canonical structure here because we've already *)
(* stated that subType_sort and FinType.sort unify via to the        *)
(* subType_finType structure.                                        *)

Definition SubFinMixin := UniqFinMixin sub_enum_uniq mem_sub_enum.Definition SubFinMixin_for (eT : eqType) of phant eT :=
  eq_rect _ Finite.mixin_of SubFinMixin eT.Canonical sig_finType := Eval hnf in FinType {x | P x} sig_finMixin.Record seq_sub : Type := SeqSub {ssval : T; ssvalP : in_mem ssval (@mem T _ s)}.Record seq_sub : Type := SeqSub {ssval : T; ssvalP : in_mem ssval (@mem T _ s)}.Record seq_sub : Type := SeqSub {ssval : T; ssvalP : in_mem ssval (@mem T _ s)}.Record seq_sub : Type := SeqSub {ssval : T; ssvalP : in_mem ssval (@mem T _ s)}.Canonical seq_sub_eqType := Eval hnf in EqType seq_sub seq_sub_eqMixin.Definition seq_sub_enum : seq seq_sub := undup (pmap insub s).

(* Specifications: *)
Lemma val_seq_sub_enum : uniq s -> map val seq_sub_enum = s.