(* Old results about [N.min] *)

Notation Nmin_choice := N.min_dec (only parsing).

(* Specifications: *)
Lemma Nmin_le_1 a b : Nleb (N.min a b) a = true.
Lemma Nmin_le_2 a b : Nleb (N.min a b) b = true.
Lemma Nmin_le_3 a b c : Nleb a (N.min b c) = true -> Nleb a b = true.
Lemma Nmin_le_4 a b c : Nleb a (N.min b c) = true -> Nleb a c = true.
Lemma Nmin_le_5 a b c : Nleb a b = true -> Nleb a c = true -> Nleb a (N.min b c) = true.
Lemma Nmin_lt_3 a b c : Nleb (N.min b c) a = false -> Nleb b a = false.
Lemma Nmin_lt_4 a b c : Nleb (N.min b c) a = false -> Nleb c a = false.