Remark expand_mult2 : forall x : nat, 2 * x = x + x.

(* Specifications: *)
Theorem lt_neq : forall x y : nat, x < y -> x <> y.
Theorem monotonic_inverse : forall f : nat -> nat, (forall x y : nat, x < y -> f x < f y) -> forall x y : nat, f x < f y -> x < y.
Theorem mult_lt : forall a b c : nat, c <> 0 -> a < b -> a * c < b * c.