advances on cpx_lfxs_conf_fle

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma
index 65237fbc1d60d4d617f5155ad3be6b0d295cc54f..b50fa075d0df92a3e145acc335fa36f88b8226d4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma
@@ -26,6 +26,25 @@ elim (frees_total L T) #f #Hf
 /2 width=8 by sle_refl, ex4_4_intro/
 qed.
 
+lemma fle_sort_length: ∀L1,L2,s1,s2. |L1| = |L2| → ⦃L1, ⋆s1⦄ ⊆ ⦃L2, ⋆s2⦄.
+/3 width=8 by lveq_length_eq, frees_sort, sle_refl, ex4_4_intro/ qed.
+
+lemma fle_gref_length: ∀L1,L2,l1,l2. |L1| = |L2| → ⦃L1, §l1⦄ ⊆ ⦃L2, §l2⦄.
+/3 width=8 by lveq_length_eq, frees_gref, sle_refl, ex4_4_intro/ qed.
+
+lemma fle_shift: ∀L1,L2. |L1| = |L2| →
+                 ∀I,T1,T2,V.  ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I}V, T2⦄ →
+                 ∀p. ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2, ⓑ{p,I}V.T2⦄.
+#L1 #L2 #H1L #I #T1 #T2 #V
+* #n #m #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
+elim (lveq_inj_length … H2L) // -H1L #H1 #H2 destruct
+lapply (lveq_inv_bind … H2L) -H2L #HL
+elim (frees_total L2 V) #g1 #Hg1
+elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+lapply (sor_inv_sle_dx … Hg) #H0g
+/4 width=10 by frees_bind, lveq_void_sn, sle_tl, sle_trans, ex4_4_intro/
+qed.
+
 lemma fle_bind_dx_sn: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
                       ∀p,I,T2. ⦃L1, V1⦄ ⊆ ⦃L2, ⓑ{p,I}V2.T2⦄.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
@@ -63,3 +82,15 @@ elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
 /4 width=5 by frees_flat, sor_inv_sle_dx, sor_tls, sle_trans/
 qed.
+
+(* Advanced forward lemmas ***************************************************)
+
+lemma fle_fwd_pair_sn: ∀I1,I2,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
+                       ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄.
+#I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 *
+#n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12
+elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
+elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
+lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
+/5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
+qed-.