{A : Type} (l : list A) (x : A) : last (l ++ [x]) = Some x. Proof. induction l as [|a l IHl] in x |- *. 1: reflexivity. destruct l. 1: reflexivity. cbn; apply IHl. Defined.
Require Import Basics.Overture Basics.Tactics Basics.PathGroupoids Basics.Trunc Require Import Types.Paths Types.Unit Types.Prod Types.Sigma Types.Sum