(* *)
(**************************************************************************)
-include "Basic-2/substitution/drop_drop.ma".
-include "Basic-2/substitution/tps.ma".
+include "Basic_2/substitution/drop_drop.ma".
+include "Basic_2/substitution/tps.ma".
(* PARTIAL SUBSTITUTION ON TERMS ********************************************)
(* Relocation properties ****************************************************)
-(* Basic-1: was: subst1_lift_lt *)
+(* Basic_1: was: subst1_lift_lt *)
lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
∀L,U1,U2,d,e. ↓[d, e] L ≡ K →
↑[d, e] T1 ≡ U1 → ↑[d, e] T2 ≡ U2 →
]
qed.
-(* Basic-1: was: subst1_lift_ge *)
+(* Basic_1: was: subst1_lift_ge *)
lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
∀L,U1,U2,d,e. ↓[d, e] L ≡ K →
↑[d, e] T1 ≡ U1 → ↑[d, e] T2 ≡ U2 →
]
qed.
-(* Basic-1: was: subst1_gen_lift_lt *)
+(* Basic_1: was: subst1_gen_lift_lt *)
lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
∀K,d,e. ↓[d, e] L ≡ K → ∀T1. ↑[d, e] T1 ≡ U1 →
dt + et ≤ d →
]
qed.
-(* Basic-1: was: subst1_gen_lift_ge *)
+(* Basic_1: was: subst1_gen_lift_ge *)
lemma tps_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
∀K,d,e. ↓[d, e] L ≡ K → ∀T1. ↑[d, e] T1 ≡ U1 →
d + e ≤ dt →
]
qed.
-(* Basic-1: was: subst1_gen_lift_eq *)
+(* Basic_1: was: subst1_gen_lift_eq *)
lemma tps_inv_lift1_eq: ∀L,U1,U2,d,e.
L ⊢ U1 [d, e] ≫ U2 → ∀T1. ↑[d, e] T1 ≡ U1 → U1 = U2.
#L #U1 #U2 #d #e #H elim H -H L U1 U2 d e