(* Constructions with proper condition for path *****************************)
lemma lift_term_proper (f) (t):
- t ϵ 𝐏 → ↑[f]t ϵ 𝐏.
+ t ϵ 𝐏 → 🠡[f]t ϵ 𝐏.
#f #t #Ht #p * #q #Hq #H0 destruct
@lift_path_proper @Ht -Ht // (**) (* auto fails *)
qed.
(* Inversions with proper condition for path ********************************)
lemma lift_term_inv_proper (f) (t):
- ↑[f]t ϵ 𝐏 → t ϵ 𝐏.
+ 🠡[f]t ϵ 𝐏 → t ϵ 𝐏.
#f #t #Ht #p #Hp
@(lift_path_inv_proper f)
@Ht -Ht @in_comp_lift_path_term // (**) (* auto fails *)