update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lfpx_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_drops.ma
index 086e71e87bd791fd522681adf3feb065a4419220..9353adda65f82154e9c1b84d4588542e7df50eb2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_drops.ma
@@ -16,25 +16,28 @@ include "basic_2/static/lfxs_drops.ma".
 include "basic_2/rt_transition/cpx_drops.ma".
 include "basic_2/rt_transition/lfpx.ma".
 
-(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
+(* UNBOUND PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *******)
 
 (* Properties with generic slicing for local environments *******************)
 
+(* Basic_2A1: uses: drop_lpx_trans *) 
 lemma drops_lfpx_trans: ∀h,G. dedropable_sn (cpx h G).
-/3 width=6 by lfxs_liftable_dedropable, cpx_lifts/ qed-.
+/3 width=6 by lfxs_liftable_dedropable_sn, cpx_lifts_sn/ qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
+(* Basic_2A1: uses: lpx_drop_conf *)
 lemma lfpx_drops_conf: ∀h,G. dropable_sn (cpx h G).
 /2 width=5 by lfxs_dropable_sn/ qed-.
 
+(* Basic_2A1: uses: lpx_drop_trans_O1 *)
 lemma lfpx_drops_trans: ∀h,G. dropable_dx (cpx h G).
 /2 width=5 by lfxs_dropable_dx/ qed-.
 
-lemma lfpx_inv_lref_sn: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →
-                        ∃∃K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
-/2 width=3 by lfxs_inv_lref_sn/ qed-.
+lemma lfpx_inv_lref_pair_sn: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
+/2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
 
-lemma lfpx_inv_lref_dx: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 →
-                        ∃∃K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
-/2 width=3 by lfxs_inv_lref_dx/ qed-.
+lemma lfpx_inv_lref_pair_dx: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
+/2 width=3 by lfxs_inv_lref_pair_dx/ qed-.