update in basic_2

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

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 deadd5cdc2908614e77668fbaa62d98328b70a02..ea09b60a7d702d2d2f1048ad0503d8139c8897a8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma
@@ -39,6 +39,15 @@ elim (lveq_inj_length … H2L) // -L2 #H1 #H2 destruct
 /2 width=3 by ex2_intro/
 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 ⊆ f2.
+#L1 #L2 #H1L #T1 #T2 #H2L #f1 #Hf1 #f2 #Hf2
+elim (fsle_frees_trans_eq … H2L … Hf2) // -L2 -T2
+/3 width=6 by frees_mono, sle_eq_repl_back1/
+qed-.
+
 (* Main properties **********************************************************)
 
 theorem fsle_trans_sn: ∀L1,L2,T1,T. ⦃L1, T1⦄ ⊆ ⦃L2, T⦄ →
@@ -65,6 +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⦄.