first results on lfpr as a base for the diamond property ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
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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/notation/relations/predsn_3.ma".
-include "basic_2/substitution/lpx_sn.ma".
-include "basic_2/reduction/cpr.ma".
-
-(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
-
-definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G).
-
-interpretation "parallel reduction (local environment, sn variant)"
-   'PRedSn G L1 L2 = (lpr G L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-(* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆.
-/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
-
-(* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 →
-                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2.
-/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
-
-lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
-
-lemma lpr_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡ K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
-/2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
-
-(* Basic properties *********************************************************)
-
-(* Note: lemma 250 *)
-lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
-/2 width=1 by lpx_sn_refl/ qed.
-
-lemma lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 →
-                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
-/2 width=1 by lpx_sn_pair/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
-/2 width=2 by lpx_sn_fwd_length/ qed-.
-
-lemma lpr_lpx: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, o] L2.
-#h #o #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/
-qed.
-
-(* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
-                                pr0_subst1_back
-*)