two cases of cpx_lfxs_conf_fle closed

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle.ma
index 7340a8abc5b8ee924dc7a1809128481f13f46003..921c37b8842e95e442f87c3bf172d961da1322ba 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle.ma
@@ -14,41 +14,22 @@
 
 include "ground_2/relocation/rtmap_id.ma".
 include "basic_2/notation/relations/subseteq_4.ma".
-include "basic_2/syntax/voids_length.ma".
+include "basic_2/syntax/lveq.ma".
 include "basic_2/static/frees.ma".
 
 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
 
-inductive fle (T1) (T2): relation lenv ≝
-| fle_intro: ∀f1,f2,L1,L2,n1,n2. ⓧ*[n1]L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 → ⓧ*[n2]L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 →
-             |L1| = |L2| → ⫱*[n1]f1 ⊆ ⫱*[n2]f2 → fle T1 T2 (ⓧ*[n1]L1) (ⓧ*[n2]L2)
-.
+definition fle: bi_relation lenv term ≝ λL1,T1,L2,T2.
+                ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 &
+                               L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
 
 interpretation "free variables inclusion (restricted closure)"
-   'SubSetEq L1 T1 L2 T2 = (fle T1 T2 L1 L2).
+   'SubSetEq L1 T1 L2 T2 = (fle L1 T1 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fle_sort: ∀L1,L2. |L1| = |L2| → ∀s1,s2. ⦃L1, ⋆s1⦄ ⊆ ⦃L2, ⋆s2⦄.
-/3 width=5 by frees_sort, sle_refl, fle_intro/ qed.
+lemma fle_sort: ∀L,s1,s2. ⦃L, ⋆s1⦄ ⊆ ⦃L, ⋆s2⦄.
+/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
 
-lemma fle_gref: ∀L1,L2. |L1| = |L2| → ∀l1,l2. ⦃L1, §l1⦄ ⊆ ⦃L2, §l2⦄.
-/3 width=5 by frees_gref, sle_refl, fle_intro/ qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact fle_inv_voids_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
-                        ∀K1,K2,n1,n2. |K1| = |K2| → L1 = ⓧ*[n1]K1 → L2 = ⓧ*[n2]K2 →
-                        ∃∃f1,f2. ⓧ*[n1]K1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & ⓧ*[n2]K2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
-#L1 #L2 #T1 #T2 * -L1 -L2
-#f1 #f2 #L1 #L2 #n1 #n2 #Hf1 #Hf2 #HL12 #Hf12 #Y1 #Y2 #x1 #x2 #HY12 #H1 #H2 destruct
->H1 in Hf1; >H2 in Hf2; #Hf2 #Hf1
-@(ex3_2_intro … Hf1 Hf2) -Hf1 -Hf2
-
-elim (voids_inj_length … H1) // -H -HL12 -HY #H1 #H2 destruct
-/2 width=5 by ex3_2_intro/
-qed-.
-
-lemma fle_inv_voids_sn: ∀L1,L2,T1,T2,n. ⦃ⓧ*[n]L1, T1⦄ ⊆ ⦃L2, T2⦄ → |L1| = |L2| →
-                        ∃∃f1,f2. ⓧ*[n]L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & ⫱*[n]f1 ⊆ f2.
-/2 width=3 by fle_inv_voids_sn_aux/ qed-.
+lemma fle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
+/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.