advances on cpx_lfxs_conf_fle

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma
index 0bd285acae1a01fd764ecca9c3915a80b0ec7239..daa61f75a8120112e3aaed003a9933f3017d867d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "basic_2/syntax/lveq_lveq.ma".
-include "basic_2/static/frees_frees.ma".
 include "basic_2/static/fle_fqup.ma".
 
 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
@@ -31,13 +30,41 @@ lapply (sle_eq_repl_back2 … Hn … Hgf2) -g2
 /2 width=6 by ex3_3_intro/
 qed-.
 
+lemma fle_frees_trans_eq: ∀L1,L2. |L1| = |L2| →
+                          ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 →
+                          ∃∃f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & f1 ⊆ f2.
+#L1 #L2 #H1L #T1 #T2 #H2L #f2 #Hf2
+elim (fle_frees_trans … H2L … Hf2) -T2 #n1 #n2 #f1 #Hf1 #H2L #Hf12
+elim (lveq_inj_length … H2L) // -L2 #H1 #H2 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
 (* Main properties **********************************************************)
-(*
-theorem fle_trans: bi_transitive … fle.
-#L1 #L #T1 #T * #f1 #f #HT1 #HT #Hf1 #L2 #T2 * #g #f2 #Hg #HT2 #Hf2
-/5 width=8 by frees_mono, sle_trans, sle_eq_repl_back2, ex3_2_intro/
+
+theorem fle_trans_sn: ∀L1,L2,T1,T. ⦃L1, T1⦄ ⊆ ⦃L2, T⦄ →
+                      ∀T2. ⦃L2, T⦄ ⊆ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
+#L1 #L2 #T1 #T
+* #m1 #m0 #g1 #g0 #Hg1 #Hg0 #Hm #Hg
+#T2
+* #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
+lapply (frees_mono … Hf0 … Hg0) -Hf0 -Hg0 #Hfg0
+elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
+lapply (sle_eq_repl_back1 … Hf … Hfg0) -f0
+/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
 qed-.
-*)
+
+theorem fle_trans_dx: ∀L1,T1,T. ⦃L1, T1⦄ ⊆ ⦃L1, T⦄ →
+                      ∀L2,T2. ⦃L1, T⦄ ⊆ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
+#L1 #T1 #T
+* #m1 #m0 #g1 #g0 #Hg1 #Hg0 #Hm #Hg
+#L2 #T2
+* #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
+lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
+elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
+lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
+/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
+qed-.
+
 theorem fle_bind_sn_ge: ∀L1,L2. |L2| ≤ |L1| →
                         ∀V1,T1,T. ⦃L1, V1⦄ ⊆ ⦃L2, T⦄ → ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2, T⦄ →
                         ∀p,I. ⦃L1, ⓑ{p,I}V1.T1⦄ ⊆ ⦃L2, T⦄.