X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffle_fle.ma;h=daa61f75a8120112e3aaed003a9933f3017d867d;hb=42705ef31dd3513a998533e02b5f20fb38dd4fb2;hp=e756b43f773e1d873c3f67fc8a583d7f481abe65;hpb=aff2f21cec89cf343297ae6bd720fc6573a3aba1;p=helm.git

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 e756b43f7..daa61f75a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fle.ma
@@ -12,63 +12,106 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/frees_frees.ma".
+include "basic_2/syntax/lveq_lveq.ma".
 include "basic_2/static/fle_fqup.ma".
 
 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma fle_inv_voids_sn_frees_dx: ∀L1,L2,T1,T2,n. ⦃ⓧ*[n]L1, T1⦄ ⊆ ⦃L2, T2⦄ →
-                                 |L1| = |L2| → ∀f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 →
-                                 ∃∃f1. ⓧ*[n]L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & ⫱*[n]f1 ⊆ f2.
-#L1 #L2 #T1 #T2 #n #H #HL12 #f2 #Hf2
-elim (fle_inv_voids_sn … H HL12) -H -HL12 #f1 #g2 #Hf1 #Hg2 #Hfg
-lapply (frees_mono … Hg2 … Hf2) -Hg2 -Hf2 #Hfg2
-lapply (sle_eq_repl_back2 … Hfg … Hfg2) -g2
+lemma fle_frees_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
+                       ∀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
+lapply (tls_eq_repl n2 … Hgf2) -Hgf2 #Hgf2
+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_bind_sn: ∀L1,L2,V1,T1,T. ⦃L1, V1⦄ ⊆ ⦃L2, T⦄ → ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2, T⦄ →
-                     ∀p,I. ⦃L1, ⓑ{p,I}V1.T1⦄ ⊆ ⦃L2, T⦄.
-#L1 #L2 #V1 #T1 #T * -L1 #f1 #x #L1 #n1 #Hf1 #Hx #HL12 #Hf1x
->voids_succ #H #p #I
-elim (fle_inv_voids_sn_frees_dx … H … Hx) -H // #f2 #Hf2
-<tls_xn #Hf2x
+
+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⦄.
+#L1 #L2 #HL #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #p #I
+elim (fle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
+elim (lveq_inj_void_sn_ge … H1n1 … H1n2) -H1n2 // #H1 #H2 #H3 destruct
 elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-/4 width=9 by fle_intro, frees_bind_void, sor_inv_sle, sor_tls/
+<tls_xn in H2n2; #H2n2
+/4 width=12 by frees_bind_void, sor_inv_sle, sor_tls, ex4_4_intro/
 qed.
 
 theorem fle_flat_sn: ∀L1,L2,V1,T1,T. ⦃L1, V1⦄ ⊆ ⦃L2, T⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T⦄ →
                      ∀I. ⦃L1, ⓕ{I}V1.T1⦄ ⊆ ⦃L2, T⦄.
-#L1 #L2 #V1 #T1 #T * -L1 #f1 #x #L1 #n1 #Hf1 #Hx #HL12 #Hf1x #H #I
-elim (fle_inv_voids_sn_frees_dx … H … Hx) -H // #f2 #Hf2 #Hf2x
+#L1 #L2 #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #I
+elim (fle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
+elim (lveq_inj … H1n1 … H1n2) -H1n2 #H1 #H2 destruct
 elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
-/4 width=9 by fle_intro, frees_flat, sor_inv_sle, sor_tls/
+/4 width=12 by frees_flat, sor_inv_sle, sor_tls, ex4_4_intro/
 qed.
-(*
-lemma fle_bind: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
-                ∀I1,I2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
-                ∀p. ⦃L1, ⓑ{p,I1}V1.T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.T2⦄.
-#L1 #L2 #V1 #V2 * #f1 #g1 #HV1 #HV2 #Hfg1 #I1 #I2 #T1 #T2 * #f2 #g2 #Hf2 #Hg2 #Hfg2 #p
+
+theorem fle_bind_eq: ∀L1,L2. |L1| = |L2| → ∀V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
+                     ∀I2,T1,T2. ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
+                     ∀p,I1. ⦃L1, ⓑ{p,I1}V1.T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.T2⦄.
+#L1 #L2 #HL #V1 #V2
+* #n1 #m1 #f1 #g1 #Hf1 #Hg1 #H1L #Hfg1 #I2 #T1 #T2
+* #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p #I1
+elim (lveq_inj_length … H1L) // #H1 #H2 destruct
+elim (lveq_inj_length … H2L) // -HL -H2L #H1 #H2 destruct
 elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
 elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-/4 width=12 by frees_bind, monotonic_sle_sor, sle_tl, ex3_2_intro/
+/4 width=15 by frees_bind_void, frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
 qed.
 
-lemma fle_flat: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
-                ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
-                ∀I1,I2. ⦃L1, ⓕ{I1}V1.T1⦄ ⊆ ⦃L2, ⓕ{I2}V2.T2⦄.
-#L1 #L2 #V1 #V2 * #f1 #g1 #HV1 #HV2 #Hfg1 #T1 #T2 * #f2 #g2 #Hf2 #Hg2 #Hfg2 #I1 #I2
-elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
-elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
-/3 width=12 by frees_flat, monotonic_sle_sor, ex3_2_intro/
+theorem fle_bind: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
+                  ∀I1,I2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
+                  ∀p. ⦃L1, ⓑ{p,I1}V1.T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.T2⦄.
+#L1 #L2 #V1 #V2
+* #n1 #m1 #f1 #g1 #Hf1 #Hg1 #H1L #Hfg1 #I1 #I2 #T1 #T2
+* #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
+elim (lveq_inv_pair_pair … H2L) -H2L #H2L #H1 #H2 destruct
+elim (lveq_inj … H2L … H1L) -H1L #H1 #H2 destruct
+elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
+elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+/4 width=15 by frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
 qed.
-*)
+
+theorem fle_flat: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
+                  ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
+                  ∀I1,I2. ⦃L1, ⓕ{I1}V1.T1⦄ ⊆ ⦃L2, ⓕ{I2}V2.T2⦄.
+/3 width=1 by fle_flat_sn, fle_flat_dx_dx, fle_flat_dx_sn/ qed-.