proposition: Lemma in_inj_comp A B C (f : B -> A) (h : C -> B) (P : pred B) (Q : pred C) : {in P &, injective f} -> {in Q &, injective h} -> {homo h : x / Q x >-> P x} -> {in Q &, injective (f \o h)}.
proof: Proof. by move=> Pf Qh QP x y xQ yQ xy; apply Qh => //; apply Pf => //; apply QP. Qed.
imports: ssreflect ssrfun