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=99b1ece949863003c3d475e1bdfb47e2f7127c28;hpb=e6282b0c066eee7329560e1929150776ca64aa4a;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 99b1ece94..9e334565f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.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⦄ →
@@ -34,6 +34,11 @@ 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 *******************)
 
 lemma lfxs_liftable_dedropable_sn: ∀R. (∀L. reflexive ? (R L)) →
@@ -45,6 +50,19 @@ 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: uses: llpx_sn_inv_lift_le llpx_sn_inv_lift_be llpx_sn_inv_lift_ge *)