(* GENERIC TERM RELOCATION **************************************************)
inductive lifts: list2 nat nat → relation term ≝
| lifts_nil : ∀T. lifts ⟠ T T
| lifts_cons: ∀T1,T,T2,des,d,e.
(* GENERIC TERM RELOCATION **************************************************)
inductive lifts: list2 nat nat → relation term ≝
| lifts_nil : ∀T. lifts ⟠ T T
| lifts_cons: ∀T1,T,T2,des,d,e.
- ∀d,e,tl. des = {d, e} :: tl →
+ ∀d,e,tl. des = {d, e} @ tl →
∃∃T. ⇧[d, e] T1 ≡ T & ⇧*[tl] T ≡ T2.
#T1 #T2 #des * -T1 -T2 -des
[ #T #d #e #tl #H destruct
∃∃T. ⇧[d, e] T1 ≡ T & ⇧*[tl] T ≡ T2.
#T1 #T2 #des * -T1 -T2 -des
[ #T #d #e #tl #H destruct
-lemma lifts_inv_cons: ∀T1,T2,d,e,des. ⇧*[{d, e} :: des] T1 ≡ T2 →
+lemma lifts_inv_cons: ∀T1,T2,d,e,des. ⇧*[{d, e} @ des] T1 ≡ T2 →
(* Basic_1: was: lift1_lref *)
lemma lifts_inv_lref1: ∀T2,des,i1. ⇧*[des] #i1 ≡ T2 →
(* Basic_1: was: lift1_lref *)
lemma lifts_inv_lref1: ∀T2,des,i1. ⇧*[des] #i1 ≡ T2 →
-lemma lifts_inv_bind1: ∀I,T2,des,V1,U1. ⇧*[des] ⓑ{I} V1. U1 ≡ T2 →
+lemma lifts_inv_bind1: ∀a,I,T2,des,V1,U1. ⇧*[des] ⓑ{a,I} V1. U1 ≡ T2 →
#T1 #T2 #des #H elim H -T1 -T2 -des // /3 width=5 by lift_simple_sn/
qed-.
(* Basic properties *********************************************************)
#T1 #T2 #des #H elim H -T1 -T2 -des // /3 width=5 by lift_simple_sn/
qed-.
(* Basic properties *********************************************************)
-lemma lifts_bind: ∀I,T2,V1,V2,des. ⇧*[des] V1 ≡ V2 →
+lemma lifts_bind: ∀a,I,T2,V1,V2,des. ⇧*[des] V1 ≡ V2 →
- ⇧*[des] ⓑ{I} V1. T1 ≡ ⓑ{I} V2. T2.
-#I #T2 #V1 #V2 #des #H elim H -V1 -V2 -des
+ ⇧*[des] ⓑ{a,I} V1. T1 ≡ ⓑ{a,I} V2. T2.
+#a #I #T2 #V1 #V2 #des #H elim H -V1 -V2 -des
[ #V #T1 #H >(lifts_inv_nil … H) -H //
| #V1 #V #V2 #des #d #e #HV1 #_ #IHV #T1 #H
elim (lifts_inv_cons … H) -H /3 width=3/
[ #V #T1 #H >(lifts_inv_nil … H) -H //
| #V1 #V #V2 #des #d #e #HV1 #_ #IHV #T1 #H
elim (lifts_inv_cons … H) -H /3 width=3/