(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
-
-axiom lift_path_after (p) (f1) (f2):
- ↑[f2]↑[f1]p = ↑[f2∘f1]p.
-(*
-#p @(path_ind_lift … p) -p // [ #n | #n #l #p | #p ] #IH #f1 #f2
-[ <lift_path_d_empty_sn <lift_path_d_empty_sn
-| <lift_path_d_lcons_sn <lift_path_d_lcons_sn
-| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
-*)
-include "delayed_updating/substitution/lift_prototerm.ma".
-
-axiom lift_term_after (t) (f1) (f2):
- ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
-
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
include "delayed_updating/syntax/prototerm_constructors.ma".
(* LIFT FOR PROTOTERM *******************************************************)
-lemma lift_iref_after_sn (f) (t) (n:pnat):
+lemma lift_iref_after_sn (f) (t:prototerm) (n:pnat):
↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
#f #t #n #p * #q #Hq #H0 destruct
@(ex2_intro … (𝗱n◗𝗺◗q))