renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfxs_length.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_length.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_length.ma
index 386e2ba8894c304c95fad915a7045eae17d4135a..bba7867c7dd52fb3d29116777d084453e82752b1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_length.ma
@@ -13,13 +13,60 @@
 (**************************************************************************)
 
 include "basic_2/relocation/lexs_length.ma".
-include "basic_2/static/lfxs.ma".
+include "basic_2/static/lfxs_drops.ma".
 
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
 (* Forward lemmas with length for local environments ************************)
 
 (* Basic_2A1: uses: llpx_sn_fwd_length *)
-lemma lfxs_fwd_length: ∀R,L1,L2,T. L1 ⦻*[R, T] L2 → |L1| = |L2|.
+lemma lfxs_fwd_length (R): ∀L1,L2,T. L1 ⪤*[R, T] L2 → |L1| = |L2|.
 #R #L1 #L2 #T * /2 width=4 by lexs_fwd_length/
 qed-.
+
+(* Properties with length for local environments ****************************)
+
+(* Basic_2A1: uses: llpx_sn_sort *)
+lemma lfxs_sort_length (R): ∀L1,L2. |L1| = |L2| → ∀s. L1 ⪤*[R, ⋆s] L2.
+#R #L1 elim L1 -L1
+[ #Y #H #s >(length_inv_zero_sn … H) -H //
+| #K1 #I1 #IH #Y #H #s
+  elim (length_inv_succ_sn … H) -H #I2 #K2 #HK12 #H destruct
+  /3 width=1 by lfxs_sort/
+]
+qed.
+
+(* Basic_2A1: uses: llpx_sn_gref *)
+lemma lfxs_gref_length (R): ∀L1,L2. |L1| = |L2| → ∀l. L1 ⪤*[R, §l] L2.
+#R #L1 elim L1 -L1
+[ #Y #H #s >(length_inv_zero_sn … H) -H //
+| #K1 #I1 #IH #Y #H #s
+  elim (length_inv_succ_sn … H) -H #I2 #K2 #HK12 #H destruct
+  /3 width=1 by lfxs_gref/
+]
+qed.
+
+lemma lfxs_unit_length (R): ∀L1,L2. |L1| = |L2| → ∀I. L1.ⓤ{I} ⪤*[R, #0] L2.ⓤ{I}.
+/3 width=3 by lfxs_unit, lexs_length_isid/ qed.
+
+(* Basic_2A1: uses: llpx_sn_lift_le llpx_sn_lift_ge *)
+lemma lfxs_lifts_bi (R): d_liftable2_sn … lifts R →
+                         ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ⪤*[R, T] K2 →
+                         ∀b,f. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
+                         ∀U. ⬆*[f] T ≘ U → L1 ⪤*[R, U] L2.
+#R #HR #L1 #L2 #HL12 #K1 #K2 #T * #f1 #Hf1 #HK12 #b #f #HLK1 #HLK2 #U #HTU
+elim (frees_total L1 U) #f2 #Hf2
+lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #Hf
+/4 width=12 by lexs_length_cfull, lexs_liftable_co_dedropable_bi, cext2_d_liftable2_sn, cfull_lift_sn, ex2_intro/
+qed-.
+
+(* Inversion lemmas with length for local environment ***********************)
+
+lemma lfxs_inv_zero_length (R): ∀Y1,Y2. Y1 ⪤*[R, #0] Y2 →
+                                ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+                                 | ∃∃I,L1,L2,V1,V2. L1 ⪤*[R, V1] L2 & R L1 V1 V2 &
+                                                    Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
+                                 | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+#R #Y1 #Y2 #H elim (lfxs_inv_zero … H) -H *
+/4 width=9 by lexs_fwd_length, ex4_5_intro, ex3_3_intro, or3_intro2, or3_intro1, or3_intro0, conj/
+qed-.