Fixpoint compact_prod (T: list Type): Type :=
  match T with
  | nil => unit
  | t :: nil => t
  | t :: T0 => (t * compact_prod T0)%type
  end.Fixpoint compact_sum (T: list Type): Type :=
  match T with
  | nil => unit
  | t :: nil => t
  | t :: T0 => (t + compact_sum T0)%type
  end.Definition compact_prod_gen {A} {F} (gen: forall a: A, F a) (l: list A): compact_prod (map F l).Definition compact_sum_gen {A} {F} (filter: A -> bool) (gen: forall a: A, F a) (l: list A): compact_sum (map F l).Definition upd_compact_prod {A} {F} (l: list A) (v: compact_prod (map F l)) (a: A) (v0: F a) (H: forall a b: A, {a = b} + {a <> b}) : compact_prod (map F l).

Lemma aux1: forall {A} {a a0: A} {l}, In a (a0 :: l) -> a <> a0 -> In a l.