X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_drops.ma;h=76adfa38b376b35601af4a65037f1bf2ca3620bc;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=40ce94c71227cb3a5a72492d04311a61a63d2985;hpb=75f395f0febd02de8e0f881d918a8812b1425c8d;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
index 40ce94c71..76adfa38b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
@@ -19,30 +19,30 @@ include "basic_2/static/lfxs.ma".
 
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
-definition dedropable_sn: predicate (relation3 lenv term term) ≝
-                          λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 →
-                          ∀K2,T. K1 ⪤*[R, T] K2 → ∀U. ⬆*[f] T ≘ U →
-                          ∃∃L2. L1 ⪤*[R, U] L2 & ⬇*[b, f] L2 ≘ K2 & L1 ≡[f] L2.
-
-definition dropable_sn: predicate (relation3 lenv term term) ≝
-                        λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 → 𝐔⦃f⦄ →
-                        ∀L2,U. L1 ⪤*[R, U] L2 → ∀T. ⬆*[f] T ≘ U →
-                        ∃∃K2. K1 ⪤*[R, T] K2 & ⬇*[b, f] L2 ≘ K2.
-
-definition dropable_dx: predicate (relation3 lenv term term) ≝
-                        λR. ∀L1,L2,U. L1 ⪤*[R, U] L2 →
-                        ∀b,f,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
-                        ∃∃K1. ⬇*[b, f] L1 ≘ K1 & K1 ⪤*[R, T] K2.
-
-definition lfxs_transitive_next: relation3 … ≝ λR1,R2,R3.
-                                 ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f →
-                                 ∀g,I,K,n. ⬇*[n] L ≘ K.ⓘ{I} → ⫯g = ⫱*[n] f →
-                                 lexs_transitive (cext2 R1) (cext2 R2) (cext2 R3) (cext2 R1) cfull g K I.
+definition f_dedropable_sn: predicate (relation3 lenv term term) ≝
+                            λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 →
+                            ∀K2,T. K1 ⪤*[R, T] K2 → ∀U. ⬆*[f] T ≘ U →
+                            ∃∃L2. L1 ⪤*[R, U] L2 & ⬇*[b, f] L2 ≘ K2 & L1 ≡[f] L2.
+
+definition f_dropable_sn: predicate (relation3 lenv term term) ≝
+                          λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 → 𝐔⦃f⦄ →
+                          ∀L2,U. L1 ⪤*[R, U] L2 → ∀T. ⬆*[f] T ≘ U →
+                          ∃∃K2. K1 ⪤*[R, T] K2 & ⬇*[b, f] L2 ≘ K2.
+
+definition f_dropable_dx: predicate (relation3 lenv term term) ≝
+                          λR. ∀L1,L2,U. L1 ⪤*[R, U] L2 →
+                          ∀b,f,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
+                          ∃∃K1. ⬇*[b, f] L1 ≘ K1 & K1 ⪤*[R, T] K2.
+
+definition f_transitive_next: relation3 … ≝ λR1,R2,R3.
+                              ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f →
+                              ∀g,I,K,n. ⬇*[n] L ≘ K.ⓘ{I} → ↑g = ⫱*[n] f →
+                              lexs_transitive (cext2 R1) (cext2 R2) (cext2 R3) (cext2 R1) cfull g K I.
 
 (* Properties with generic slicing for local environments *******************)
 
 lemma lfxs_liftable_dedropable_sn: ∀R. (∀L. reflexive ? (R L)) →
-                                   d_liftable2_sn … lifts R → dedropable_sn R.
+                                   d_liftable2_sn … lifts R → f_dedropable_sn R.
 #R #H1R #H2R #b #f #L1 #K1 #HLK1 #K2 #T * #f1 #Hf1 #HK12 #U #HTU
 elim (frees_total L1 U) #f2 #Hf2
 lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #Hf
@@ -50,7 +50,7 @@ elim (lexs_liftable_co_dedropable_sn … HLK1 … HK12 … Hf) -f1 -K1
 /3 width=6 by cext2_d_liftable2_sn, cfull_lift_sn, ext2_refl, ex3_intro, ex2_intro/
 qed-.
 
-lemma lfxs_trans_next: ∀R1,R2,R3. lfxs_transitive R1 R2 R3 → lfxs_transitive_next R1 R2 R3.
+lemma lfxs_trans_next: ∀R1,R2,R3. lfxs_transitive R1 R2 R3 → f_transitive_next R1 R2 R3.
 #R1 #R2 #R3 #HR #f #L1 #T #Hf #g #I1 #K1 #n #HLK #Hgf #I #H
 generalize in match HLK; -HLK elim H -I1 -I
 [ #I #_ #L2 #_ #I2 #H
@@ -67,7 +67,7 @@ qed.
 
 (* Basic_2A1: uses: llpx_sn_inv_lift_le llpx_sn_inv_lift_be llpx_sn_inv_lift_ge *)
 (* Basic_2A1: was: llpx_sn_drop_conf_O *)
-lemma lfxs_dropable_sn: ∀R. dropable_sn R.
+lemma lfxs_dropable_sn: ∀R. f_dropable_sn R.
 #R #b #f #L1 #K1 #HLK1 #H1f #L2 #U * #f2 #Hf2 #HL12 #T #HTU
 elim (frees_total K1 T) #f1 #Hf1
 lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #H2f
@@ -77,7 +77,7 @@ qed-.
 
 (* Basic_2A1: was: llpx_sn_drop_trans_O *)
 (* Note: the proof might be simplified *)
-lemma lfxs_dropable_dx: ∀R. dropable_dx R.
+lemma lfxs_dropable_dx: ∀R. f_dropable_dx R.
 #R #L1 #L2 #U * #f2 #Hf2 #HL12 #b #f #K2 #HLK2 #H1f #T #HTU
 elim (drops_isuni_ex … H1f L1) #K1 #HLK1
 elim (frees_total K1 T) #f1 #Hf1