include "basic_2/rt_transition/cpx_drops.ma".
include "basic_2/rt_transition/rpx.ma".
-(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+(* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
(* Properties with generic slicing for local environments *******************)
-lemma rpx_lifts_sn (h) (G): f_dedropable_sn (cpx h G).
+lemma rpx_lifts_sn (G): f_dedropable_sn (cpx G).
/3 width=6 by rex_liftable_dedropable_sn, cpx_lifts_sn/ qed-.
(* Inversion lemmas with generic slicing for local environments *************)
-lemma rpx_inv_lifts_sn (h) (G): f_dropable_sn (cpx h G).
+lemma rpx_inv_lifts_sn (G): f_dropable_sn (cpx G).
/2 width=5 by rex_dropable_sn/ qed-.
-lemma rpx_inv_lifts_dx (h) (G): f_dropable_dx (cpx h G).
+lemma rpx_inv_lifts_dx (G): f_dropable_dx (cpx G).
/2 width=5 by rex_dropable_dx/ qed-.
-lemma rpx_inv_lifts_bi (h) (G):
- ∀L1,L2,U. ❪G,L1❫ ⊢ ⬈[h,U] L2 → ∀b,f. 𝐔❪f❫ →
- ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
- ∀T. ⇧*[f]T ≘ U → ❪G,K1❫ ⊢ ⬈[h,T] K2.
+lemma rpx_inv_lifts_bi (G):
+ ∀L1,L2,U. ❪G,L1❫ ⊢ ⬈[U] L2 → ∀b,f. 𝐔❪f❫ →
+ ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
+ ∀T. ⇧*[f]T ≘ U → ❪G,K1❫ ⊢ ⬈[T] K2.
/2 width=10 by rex_inv_lifts_bi/ qed-.