proposition: Lemma InjectsInto_trans X Y Z : InjectsInto X Y -> InjectsInto Y Z -> InjectsInto X Z.
proof: Proof. intros H1 H2. eapply merely_destruct; try apply H1. intros [f Hf]. eapply merely_destruct; try apply H2. intros [g Hg]. apply tr. exists (fun x => g (f x)). intros x x' H. now apply Hf, Hg. Qed.
imports: HoTT.TruncType HoTT.Classes.interfaces.abstract_algebra