milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tprs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tprs.etc
deleted file mode 100644 (file)
index 492b390..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tprs.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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( T1 ➡ * break term 46 T2 )"
-   non associative with precedence 45
-   for @{ 'PRedStar $T1 $T2 }.
-
-include "basic_2/reducibility/tpr.ma".
-
-(* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
-
-(* Basic_1: includes: pr1_pr0 *)
-definition tprs: relation term ≝ TC … tpr.
-
-interpretation "context-free parallel computation (term)"
-   'PRedStar T1 T2 = (tprs T1 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma tprs_ind: ∀T1. ∀R:predicate term. R T1 →
-                (∀T,T2. T1 ➡* T → T ➡ T2 → R T → R T2) →
-                ∀T2. T1 ➡* T2 → R T2.
-#T1 #R #HT1 #IHT1 #T2 #HT12
-@(TC_star_ind … HT1 IHT1 … HT12) //
-qed-.
-
-lemma tprs_ind_dx: ∀T2. ∀R:predicate term. R T2 →
-                   (∀T1,T. T1 ➡ T → T ➡* T2 → R T → R T1) →
-                   ∀T1. T1 ➡* T2 → R T1.
-#T2 #R #HT2 #IHT2 #T1 #HT12
-@(TC_star_ind_dx … HT2 IHT2 … HT12) //
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma tprs_refl: reflexive … tprs.
-/2 width=1/ qed.
-
-lemma tpr_tprs: ∀T1,T2. T1 ➡ T2 → T2 ➡* T2.
-/2 width=1/ qed.
-
-lemma tprs_strap1: ∀T1,T,T2. T1 ➡* T → T ➡ T2 → T1 ➡* T2.
-/2 width=3/ qed.
-
-lemma tprs_strap2: ∀T1,T,T2. T1 ➡ T → T ➡* T2 → T1 ➡* T2.
-/2 width=3/ qed.
-
-(* Basic_1: was only: pr1_head_1 *)
-lemma tprs_pair_sn: ∀I,T1,T2. T1 ➡ T2 → ∀V1,V2. V1 ➡* V2 →
-                    ②{I} V1. T1 ➡* ②{I} V2. T2.
-* [ #a ] #I #T1 #T2 #HT12 #V1 #V2 #H @(tprs_ind … H) -V2
-[1,3: /3 width=1/
-|2,4: #V #V2 #_ #HV2 #IHV1
-      @(tprs_strap1 … IHV1) -IHV1 /2 width=1/
-]
-qed.
-
-(* Basic_1: was only: pr1_head_2 *)
-lemma tprs_pair_dx: ∀I,V1,V2. V1 ➡ V2 → ∀T1,T2. T1 ➡* T2 →
-                    ②{I} V1. T1 ➡* ②{I} V2. T2.
-* [ #a ] #I #V1 #V2 #HV12 #T1 #T2 #H @(tprs_ind … H) -T2
-[1,3: /3 width=1/
-|2,4: #T #T2 #_ #HT2 #IHT1
-      @(tprs_strap1 … IHT1) -IHT1 /2 width=1/
-]
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma tprs_inv_atom1: ∀U2,k. ⋆k ➡* U2 → U2 = ⋆k.
-#U2 #k #H @(tprs_ind … H) -U2 //
-#U #U2 #_ #HU2 #IHU1 destruct
->(tpr_inv_atom1 … HU2) -HU2 //
-qed-.
-
-lemma tprs_inv_cast1: ∀W1,T1,U2. ⓝW1.T1 ➡* U2 → T1 ➡* U2 ∨
-                      ∃∃W2,T2. W1 ➡* W2 & T1 ➡* T2 & U2 = ⓝW2.T2.
-#W1 #T1 #U2 #H @(tprs_ind … H) -U2 /3 width=5/
-#U #U2 #_ #HU2 * /3 width=3/ *
-#W #T #HW1 #HT1 #H destruct
-elim (tpr_inv_cast1 … HU2) -HU2 /3 width=3/ *
-#W2 #T2 #HW2 #HT2 #H destruct /4 width=5/
-qed-.