(** By using [inversion], we can also apply the principle of explosion to "obviously contradictory" hypotheses involving inductive properties. For example: *)

(* Specifications: *)
Theorem one_not_even : ~ ev 1.
(* ================================================================= *)
(** ** Induction on Evidence *)
(** If this looks familiar, it is no coincidence: We've encountered similar problems in the [Induction] chapter, when trying to use case analysis to prove results that required induction.  And once again the solution is... induction!  The behavior of [induction] on evidence is the same as its behavior on data: It causes Coq to generate one subgoal for each constructor that could have used to build that evidence, while providing an induction hypotheses for each recursive occurrence of the property in question. *)
(** Let's try our current lemma again: *)
Lemma ev_even : forall n,
ev n -> exists k, n = double k.