milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / ltprs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltprs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltprs.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/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-.