X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffsle_fsle.ma;h=1b220af99d6126b91a6550b55bf627faae6118c1;hp=9468fe1c700b76b3c8ad47656d6629db6c5e2227;hb=222044da28742b24584549ba86b1805a87def070;hpb=f7296f9cf2ee73465a374942c46b138f35c42ccb

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma
index 9468fe1c7..1b220af99 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma
@@ -20,8 +20,8 @@ include "basic_2/static/fsle_fqup.ma".
 (* Advanced inversion lemmas ************************************************)
 
 lemma fsle_frees_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
-                        ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 →
-                        ∃∃n1,n2,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 &
+                        ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≘ f2 →
+                        ∃∃n1,n2,f1. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 &
                                     L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #f1 #g2 #Hf1 #Hg2 #HL #Hn #f2 #Hf2
 lapply (frees_mono … Hg2 … Hf2) -Hg2 -Hf2 #Hgf2
@@ -31,8 +31,8 @@ lapply (sle_eq_repl_back2 … Hn … Hgf2) -g2
 qed-.
 
 lemma fsle_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.
+                           ∀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 (fsle_frees_trans … H2L … Hf2) -T2 #n1 #n2 #f1 #Hf1 #H2L #Hf12
 elim (lveq_inj_length … H2L) // -L2 #H1 #H2 destruct
@@ -41,7 +41,7 @@ qed-.
 
 lemma fsle_inv_frees_eq: ∀L1,L2. |L1| = |L2| →
                          ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
-                         ∀f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 → ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 →
+                         ∀f1. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 → ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≘ f2 →
                          f1 ⊆ f2.
 #L1 #L2 #H1L #T1 #T2 #H2L #f1 #Hf1 #f2 #Hf2
 elim (fsle_frees_trans_eq … H2L … Hf2) // -L2 -T2
@@ -74,6 +74,19 @@ lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
 /4 width=10 by sle_tls, sle_trans, ex4_4_intro/
 qed-.
 
+theorem fsle_trans_rc: ∀L1,L,T1,T. |L1| = |L| → ⦃L1, T1⦄ ⊆ ⦃L, T⦄ →
+                       ∀L2,T2. |L| = |L2| → ⦃L, T⦄ ⊆ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
+#L1 #L #T1 #T #HL1
+* #m1 #m0 #g1 #g0 #Hg1 #Hg0 #Hm #Hg
+#L2 #T2 #HL2
+* #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
+elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
+lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
+/3 width=10 by lveq_length_eq, sle_trans, ex4_4_intro/
+qed-.
+
 theorem fsle_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⦄.