milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltprs.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltprs.etc
new file mode 100644 (file)
index 0000000..8e0c32e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltprs.etc
@@ -0,0 +1,90 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/reducibility/ltpr.ma".
+include "basic_2/computation/tprs.ma".
+
+(* CONTEXT-FREE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS ******************)
+
+definition ltprs: relation lenv ≝ TC … ltpr.
+
+interpretation
+  "context-free parallel computation (environment)"
+  'PRedStar L1 L2 = (ltprs L1 L2).
+
+(* Basic eliminators ********************************************************)
+
+lemma ltprs_ind: ∀L1. ∀R:predicate lenv. R L1 →
+                 (∀L,L2. L1 ➡* L → L ➡ L2 → R L → R L2) →
+                 ∀L2. L1 ➡* L2 → R L2.
+#L1 #R #HL1 #IHL1 #L2 #HL12
+@(TC_star_ind … HL1 IHL1 … HL12) //
+qed-.
+
+lemma ltprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
+                    (∀L1,L. L1 ➡ L → L ➡* L2 → R L → R L1) →
+                    ∀L1. L1 ➡* L2 → R L1.
+#L2 #R #HL2 #IHL2 #L1 #HL12
+@(TC_star_ind_dx … HL2 IHL2 … HL12) //
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma ltprs_refl: reflexive … ltprs.
+/2 width=1/ qed.
+
+lemma ltpr_ltprs: ∀L1,L2. L1 ➡ L2 → L1 ➡* L2.
+/2 width=1/ qed.
+
+lemma ltprs_strap1: ∀L1,L,L2. L1 ➡* L → L ➡ L2 → L1 ➡* L2.
+/2 width=3/ qed.
+
+lemma ltprs_strap2: ∀L1,L,L2. L1 ➡ L → L ➡* L2 → L1 ➡* L2.
+/2 width=3/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma ltprs_inv_atom1: ∀L2. ⋆ ➡* L2 → L2 = ⋆.
+#L2 #H @(ltprs_ind … H) -L2 //
+#L #L2 #_ #HL2 #IHL1 destruct
+>(ltpr_inv_atom1 … HL2) -L2 //
+qed-.
+
+lemma ltprs_inv_pair1: ∀I,K1,L2,V1. K1. ⓑ{I} V1 ➡* L2 →
+                       ∃∃K2,V2. K1 ➡* K2 & V1 ➡* V2 & L2 = K2. ⓑ{I} V2.
+#I #K1 #L2 #V1 #H @(ltprs_ind … H) -L2 /2 width=5/
+#L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct
+elim (ltpr_inv_pair1 … HL2) -HL2 #K2 #V2 #HK2 #HV2 #H destruct /3 width=5/
+qed-.
+
+lemma ltprs_inv_atom2: ∀L1. L1 ➡* ⋆ → L1 = ⋆.
+#L1 #H @(ltprs_ind_dx … H) -L1 //
+#L1 #L #HL1 #_ #IHL2 destruct
+>(ltpr_inv_atom2 … HL1) -L1 //
+qed-.
+
+lemma ltprs_inv_pair2: ∀I,L1,K2,V2. L1 ➡* K2. ⓑ{I} V2 →
+                       ∃∃K1,V1. K1 ➡* K2 & V1 ➡* V2 & L1 = K1. ⓑ{I} V1.
+#I #L1 #K2 #V2 #H @(ltprs_ind_dx … H) -L1 /2 width=5/
+#L1 #L #HL1 #_ * #K #V #HK2 #HV2 #H destruct
+elim (ltpr_inv_pair2 … HL1) -HL1 #K1 #V1 #HK1 #HV1 #H destruct /3 width=5/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma ltprs_fwd_length: ∀L1,L2. L1 ➡* L2 → |L1| = |L2|.
+#L1 #L2 #H @(ltprs_ind … H) -L2 //
+#L #L2 #_ #HL2 #IHL1
+>IHL1 -L1 >(ltpr_fwd_length … HL2) -HL2 //
+qed-.