lref case closed in cpx_lfxs_conf_fle

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma
index ff0b8872d6f403b0a2e7e8c6295e3734c57aee63..c64e197ef122fef84eff1c9b93795e5fbd5e263c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/syntax/lveq_length.ma".
 include "basic_2/static/frees_drops.ma".
 include "basic_2/static/fle.ma".
 
@@ -19,13 +20,38 @@ include "basic_2/static/fle.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma fle_bind_dx: ∀T,U. ⬆*[1] T ≡ U →
-                   ∀p,I,L,V. ⦃L, T⦄ ⊆ ⦃L, ⓑ{p,I}V.U⦄.
-#T #U #HTU #p #I #L #V
-elim (frees_total L V) #f1 #Hf1
-elim (frees_total L T) #f2 #Hf2
-elim (sor_isfin_ex f1 f2) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-lapply (sor_inv_sle_dx … Hf) #Hf0
-elim (lveq_refl L) #n #HL
-/6 width=8 by frees_lifts_SO, frees_bind, drops_refl, drops_drop, sle_tls, ex4_4_intro/
+lemma fle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≡ U1 → ∀L1,L2. |L2| ≤ |L1| →
+                    ∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄.
+#T1 #U1 #HTU1 #L1 #L2 #H1L #T2
+* #n #m #f #g #Hf #Hg #H2L #Hfg
+lapply (lveq_length_fwd_dx … H2L ?) // -H1L #H destruct
+lapply (frees_lifts_SO (Ⓣ) (L1.ⓧ) … HTU1 … Hf)
+[ /3 width=4 by drops_refl, drops_drop/ ] -T1 #Hf
+@(ex4_4_intro … Hf Hg) /2 width=4 by lveq_void_sn/ (**) (* explict constructor *)
+qed-.
+
+lemma fle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ⦃K1, T1⦄ ⊆ ⦃K2, T2⦄ →
+                    ∀U1,U2. ⬆*[1] T1 ≡ U1 → ⬆*[1] T2 ≡ U2 →
+                    ∀I1,I2.  ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄.
+#K1 #K2 #HK #T1 #T2
+* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
+#U1 #U2 #HTU1 #HTU2 #I1 #I2
+elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
+/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/
 qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma fle_inv_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≡ U1 →
+                        ∀I1,I2,L1,L2,V1,V2,U2. ⦃L1.ⓑ{I1}V1,U1⦄ ⊆ ⦃L2.ⓑ{I2}V2, U2⦄ →
+                        ∀p. ⦃L1, T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.U2⦄.
+#T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2
+* #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
+elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
+elim (frees_total L2 V2) #g1 #Hg1
+elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
+[1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2
+lapply (sor_inv_sle_dx … Hg) #H0g
+/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/
+qed-.