Hypothesis decA : forall x y : A, {x = y}+{x <> y}.

(* Specifications: *)
Lemma count_occ_repeat_eq x y n : x = y -> count_occ decA (repeat y n) x = n.
Lemma count_occ_repeat_neq x y n : x <> y -> count_occ decA (repeat y n) x = 0.
Lemma count_occ_unique x l : count_occ decA l x = length l -> l = repeat x (length l).
Lemma count_occ_repeat_excl x l :
(forall y, y <> x -> count_occ decA l y = 0) -> l = repeat x (length l).
Lemma count_occ_sgt l x : l = [x] <->
count_occ decA l x = 1 /\ forall y, y <> x -> count_occ decA l y = 0.
Lemma nth_repeat a m n :
nth n (repeat a m) a = a.
Lemma nth_repeat_lt a m n d :
n < m ->
nth n (repeat a m) d = a.
Lemma nth_error_repeat a m n :
n < m -> nth_error (repeat a m) n = Some a.