From 14fef03bcc79583593a129bf9c68bdf690a10eb7 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 10 Aug 2011 11:13:18 +0000
Subject: [PATCH] some refactoring

---
 matita/matita/lib/lambda-delta/ground.ma      |  3 +
 .../lib/lambda-delta/reduction/pr_subst.ma    | 62 -------------------
 .../lib/lambda-delta/substitution/tps_tps.ma  |  3 -
 3 files changed, 3 insertions(+), 65 deletions(-)
 delete mode 100644 matita/matita/lib/lambda-delta/reduction/pr_subst.ma

diff --git a/matita/matita/lib/lambda-delta/ground.ma b/matita/matita/lib/lambda-delta/ground.ma
index e09e7d47a..ed5876107 100644
--- a/matita/matita/lib/lambda-delta/ground.ma
+++ b/matita/matita/lib/lambda-delta/ground.ma
@@ -144,6 +144,9 @@ lemma arith_h1: ∀a1,a2,b,c1. c1 ≤ a1 → c1 ≤ b →
 #a1 #a2 #b #c1 #H1 #H2 <le_plus_minus_comm /2/
 qed.
 
+lemma arith_i2: ∀a,c1,c2. c1 + c2 ≤ a → c1 + c2 + (a - c1 - c2) = a.
+/2/ qed.
+
 lemma arith_z1: ∀a,b,c1. a + c1 - b - c1 = a - b.
 // qed.
 
diff --git a/matita/matita/lib/lambda-delta/reduction/pr_subst.ma b/matita/matita/lib/lambda-delta/reduction/pr_subst.ma
deleted file mode 100644
index c762091a5..000000000
--- a/matita/matita/lib/lambda-delta/reduction/pr_subst.ma
+++ /dev/null
@@ -1,62 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "lambda-delta/substitution/lift_main.ma".
-include "lambda-delta/substitution/subst_defs.ma".
-include "lambda-delta/reduction/pr_defs.ma".
-
-lemma subst_pr: ∀d,e,L,T1,U2. L ⊢ ↓[d,e] T1 ≡ U2 → ∀T2. ↑[d,e] U2 ≡ T2 →
-                L ⊢ T1 ⇒ T2.
-#d #e #L #T1 #U2 #H elim H -H d e L T1 U2
-[ #L #k #d #e #X #HX
-  lapply (lift_inv_sort1 … HX) -HX #HX destruct -X //
-| #L #i #d #e #Hid #X #HX
-  lapply (lift_inv_lref1_lt … HX Hid) -HX #HX destruct -X //
-| #L #K #V #U1 #U2 #i #d #e #Hdi #Hide #HLK #_ #HU12 #IHVU1 #U #HU2
-  lapply (lift_trans_be … HU12 … HU2 ? ?) // -HU12 HU2 U2 #HU1
-  elim (lift_free … HU1 0 (d+e-i-1) ? ? ?) -HU1 // #U2 #HU12 >arith6 // #HU2
-  @pr_delta [4,5,6: /2/ |1,2,3: skip ] (**) (* /2/ *)
-| #L #i #d #e #Hdei #X #HX
-  lapply (lift_inv_lref1_ge … HX ?) -HX /2/ #HX destruct -X;
-  >arith7 /2/
-| #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_bind1 … HX) -HX #V #T #HV2 #HT2 #HX destruct -X /3/
-| #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_flat1 … HX) -HX #V #T #HV2 #HT2 #HX destruct -X /3/
-]
-qed.
-(*
-lemma pr_subst_pr: ∀L,T1,T. L ⊢ T1 ⇒ T → ∀d,e,U. L ⊢ ↓[d,e] T ≡ U →
-                   ∀T2. ↑[d,e] U ≡ T2 → L ⊢ T1 ⇒ T2.
-#L #T1 #T #H elim H -H L T1 T
-[ /2 width=5/
-| /2 width=5/
-| #L #I #V1 #V2 #T1 #T2 #HV12 #HT12 #IHV12 #IHT12 #d #e #X2 #HX2 #X1 #HX1 
-  elim (subst_inv_bind1 … HX2) -HX2 #V3 #T3 #HV23 #HT23 #H destruct -X2;
-  elim (lift_inv_bind1 … HX1) -HX1 #V4 #T4 #HV34 #HT34 #H destruct -X1;
-  @pr_bind /2 width=5/ @IHT12 
-| #L #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X2 #HX2 #X1 #HX1 
-  elim (subst_inv_flat1 … HX2) -HX2 #V3 #T3 #HV23 #HT23 #H destruct -X2;
-  elim (lift_inv_flat1 … HX1) -HX1 #V4 #T4 #HV34 #HT34 #H destruct -X1;
-  /3 width=5/
-| #L #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X2 #HX2 #X1 #HX1
-  elim (subst_inv_bind1 … HX2) -HX2 #V3 #T3 #HV23 #HT23 #H destruct -X2;
-  elim (lift_inv_bind1 … HX1) -HX1 #V4 #T4 #HV34 #HT34 #H destruct -X1;
-  @pr_beta /2 width=5/ @IHT12
-| #L #K #V1 #V2 #V #i #HLK #HV12 #HV2 #IHV12 #d #e #U #HVU #U0 #HU0
-  lapply (lift_free … HU0 0 (i + 1 + e) ? ? ?) // 
-  
-  
-  @pr_delta [4: // |1,2: skip |6: 
-*) 
diff --git a/matita/matita/lib/lambda-delta/substitution/tps_tps.ma b/matita/matita/lib/lambda-delta/substitution/tps_tps.ma
index 8d801d50e..c1faa23f4 100644
--- a/matita/matita/lib/lambda-delta/substitution/tps_tps.ma
+++ b/matita/matita/lib/lambda-delta/substitution/tps_tps.ma
@@ -11,9 +11,6 @@
 
 include "lambda-delta/substitution/tps_split.ma".
 
-lemma arith_i2: ∀a,c1,c2. c1 + c2 ≤ a → c1 + c2 + (a - c1 - c2) = a.
-/2/ qed.
-
 (* PARTIAL SUBSTITUTION ON TERMS ********************************************)
 
 (* Main properties **********************************************************)
-- 
2.39.2