diff --git a/theories/telescopes.v b/theories/telescopes.v index 40011932891791c64e08a7c3f6f364d1d1b36af8..8e68e3cc27d3c8a740471fee8256264107c019e0 100644 --- a/theories/telescopes.v +++ b/theories/telescopes.v @@ -106,19 +106,19 @@ Qed. (** We can define the identity function and composition of the [-t>] function space. *) -Definition tele_id {TT : tele} : TT -t> TT := tele_bind id. +Definition tele_fun_id {TT : tele} : TT -t> TT := tele_bind id. -Lemma tele_id_eq {TT : tele} (x : TT) : - tele_id x = x. -Proof. unfold tele_id. rewrite tele_app_bind. done. Qed. +Lemma tele_fun_id_eq {TT : tele} (x : TT) : + tele_fun_id x = x. +Proof. unfold tele_fun_id. rewrite tele_app_bind. done. Qed. -Definition tele_compose {TT1 TT2 TT3 : tele} : +Definition tele_fun_compose {TT1 TT2 TT3 : tele} : (TT2 -t> TT3) → (TT1 -t> TT2) → (TT1 -t> TT3) := λ t1 t2, tele_bind (compose (tele_app t1) (tele_app t2)). -Lemma tele_compose_eq {TT1 TT2 TT3 : tele} (f : TT2 -t> TT3) (g : TT1 -t> TT2) x : - tele_compose f g $ x = (f ∘ g) x. -Proof. unfold tele_compose. rewrite tele_app_bind. done. Qed. +Lemma tele_fun_compose_eq {TT1 TT2 TT3 : tele} (f : TT2 -t> TT3) (g : TT1 -t> TT2) x : + tele_fun_compose f g $ x = (f ∘ g) x. +Proof. unfold tele_fun_compose. rewrite tele_app_bind. done. Qed. (** Notation *) Notation "'[tele' x .. z ]" :=