update in basic_2 and ground_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 d49e4e01d71167d430e4942ea6b0050a2d2a823b..94ed9d8bf7212b6dcfeda9a830ba838eb9c41e38 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
@@ -20,21 +20,24 @@ include "basic_2/rt_transition/lfpx.ma".
 
 (* 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_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-.