X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_drops.ma;h=9e334565f386fc740e66a8f1bf9b6b19c905300e;hb=268e7f336d036f77ffc9663358e9afda92b97730;hp=8edb37e99bb36f9f918343c383ee5d98bed91993;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4;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 8edb37e99..9e334565f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/relocation/drops_cext2.ma".
 include "basic_2/relocation/drops_lexs.ma".
-include "basic_2/relocation/drops_ext2.ma".
 include "basic_2/static/frees_drops.ma".
 include "basic_2/static/lfxs.ma".
 
@@ -22,7 +22,7 @@ include "basic_2/static/lfxs.ma".
 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.
+                          ∃∃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⦄ →
@@ -34,9 +34,13 @@ definition dropable_dx: predicate (relation3 lenv term term) ≝
                         ∀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.
+
 (* Properties with generic slicing for local environments *******************)
 
-(* Basic_2A1: includes: llpx_sn_lift_le llpx_sn_lift_ge *)
 lemma lfxs_liftable_dedropable_sn: ∀R. (∀L. reflexive ? (R L)) →
                                    d_liftable2_sn … lifts R → dedropable_sn R.
 #R #H1R #H2R #b #f #L1 #K1 #HLK1 #K2 #T * #f1 #Hf1 #HK12 #U #HTU
@@ -46,9 +50,22 @@ 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.
+#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
+  lapply (ext2_inv_unit_sn … H) -H #H destruct
+  /2 width=1 by ext2_unit/
+| #I #V1 #V #HV1 #HLK1 #L2 #HL12 #I2 #H
+  elim (ext2_inv_pair_sn … H) -H #V2 #HV2 #H destruct
+  elim (frees_inv_drops_next … Hf … HLK1 … Hgf) -f -HLK1 #f #Hf #Hfg
+  /5 width=5 by ext2_pair, sle_lexs_trans, ex2_intro/
+]
+qed.
+
 (* Inversion lemmas with generic slicing for local environments *************)
 
-(* Basic_2A1: restricts: llpx_sn_inv_lift_le llpx_sn_inv_lift_be llpx_sn_inv_lift_ge *)
+(* 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.
 #R #b #f #L1 #K1 #HLK1 #H1f #L2 #U * #f2 #Hf2 #HL12 #T #HTU
@@ -69,13 +86,13 @@ elim (lexs_co_dropable_dx … HL12 … HLK2 … H2f) -L2
 /4 width=9 by frees_inv_lifts, ex2_intro/
 qed-.
 
-(* Basic_2A1: was: llpx_sn_inv_lift_O *)
-lemma lfxs_inv_lifts_bi: ∀R,L1,L2,U. L1 ⪤*[R, U] L2 →
-                         ∀K1,K2,i. ⬇*[i] L1 ≡ K1 → ⬇*[i] L2 ≡ K2 →
-                         ∀T. ⬆*[i] T ≡ U → K1 ⪤*[R, T] K2.
-#R #L1 #L2 #U #HL12 #K1 #K2 #i #HLK1 #HLK2 #T #HTU
+(* Basic_2A1: uses: llpx_sn_inv_lift_O *)
+lemma lfxs_inv_lifts_bi: ∀R,L1,L2,U. L1 ⪤*[R, U] L2 → ∀b,f. 𝐔⦃f⦄ → 
+                         ∀K1,K2. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
+                         ∀T. ⬆*[f] T ≡ U → K1 ⪤*[R, T] K2.
+#R #L1 #L2 #U #HL12 #b #f #Hf #K1 #K2 #HLK1 #HLK2 #T #HTU
 elim (lfxs_dropable_sn … HLK1 … HL12 … HTU) -L1 -U // #Y #HK12 #HY
-lapply (drops_mono … HY … HLK2) -L2 -i #H destruct //
+lapply (drops_mono … HY … HLK2) -b -f -L2 #H destruct //
 qed-.
 
 lemma lfxs_inv_lref_pair_sn: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →