proposition: Lemma is_guarded_inj_spec' {A B: Type} (P: A -> Prop) (f: A -> B): is_guarded_inj P f -> forall a1 a2: A, P a1 -> P a2 -> a1 <> a2 -> f a1 <> f a2.
proof: Proof. intros. specialize (is_guarded_inj_spec _ _ H a1 a2 H0 H1). intros ? ?. apply H2. apply H3; auto. Qed.
imports: Coq.Relations.Relation_Definitions Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.Relation_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext