milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / cpr / ltpss_dx_tps.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpss_dx_tps.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpss_dx_tps.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpss_dx_tps.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/unfold/ltpss_dx_ldrop.ma".
+
+(* DX PARALLEL UNFOLD ON LOCAL ENVIRONMENTS *********************************)
+
+(* Properties concerning partial substitution on terms **********************)
+
+lemma ltpss_dx_tps_conf_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶ [d2, e2] U2 →
+                            ∀L1,d1,e1. L0 ▶* [d1, e1] L1 → d1 + e1 ≤ d2 →
+                            L1 ⊢ T2 ▶ [d2, e2] U2.
+#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
+[ //
+| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01 #Hde1d2
+  lapply (transitive_le … Hde1d2 Hdi2) -Hde1d2 #Hde1i2
+  lapply (ltpss_dx_ldrop_conf_ge … HL01 … HLK0 ?) -L0 // /2 width=4/
+| #L0 #a #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01 #Hde1d2
+  @tps_bind [ /2 width=4/ | @IHTU2 -IHTU2 -IHVW2 [3: /2 by ltpss_dx_tpss1/ |1,2: skip | /2 width=1/ ] ] (**) (* explicit constructor *)
+| /3 width=4/
+]
+qed.
+
+lemma ltpss_dx_tps_trans_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶ [d2, e2] U2 →
+                             ∀L1,d1,e1. L1 ▶* [d1, e1] L0 → d1 + e1 ≤ d2 →
+                             L1 ⊢ T2 ▶ [d2, e2] U2.
+#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
+[ //
+| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10 #Hde1d2
+  lapply (transitive_le … Hde1d2 Hdi2) -Hde1d2 #Hde1i2
+  lapply (ltpss_dx_ldrop_trans_ge … HL10 … HLK0 ?) -L0 // /2 width=4/
+| #L0 #a #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10 #Hde1d2
+  @tps_bind [ /2 width=4/ | @IHTU2 -IHTU2 -IHVW2 [3: /2 by ltpss_dx_tpss1/ |1,2: skip | /2 width=1/ ] ] (**) (* explicit constructor *)
+| /3 width=4/
+]
+qed.