From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 11 Mar 2012 19:30:07 +0000 (+0000)
Subject: - context-sensitive computation: more properties
X-Git-Tag: make_still_working~1861
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=11a20b624a4b5ed18008678cf6cd46dd9a32634d;p=helm.git

- context-sensitive computation: more properties
- context-sensitive reduction: bug fix in a lemma's name
- some annotations added
---

diff --git a/matita/matita/contribs/lambda_delta/basic_2/basic_1.txt b/matita/matita/contribs/lambda_delta/basic_2/basic_1.txt
index 633e77f54..42357fb88 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/basic_1.txt
+++ b/matita/matita/contribs/lambda_delta/basic_2/basic_1.txt
@@ -255,10 +255,6 @@ pr3/fwd pr3_gen_lref
 pr3/fwd pr3_gen_void
 pr3/fwd pr3_gen_bind
 pr3/iso pr3_iso_appls_abbr
-pr3/iso pr3_iso_appl_bind
-pr3/iso pr3_iso_appls_appl_bind
-pr3/iso pr3_iso_appls_bind
-pr3/iso pr3_iso_beta
 pr3/iso pr3_iso_appls_beta
 pr3/pr1 pr3_pr1
 pr3/pr3 pr3_strip
@@ -267,7 +263,6 @@ pr3/props pr3_head_1
 pr3/props pr3_head_2
 pr3/props pr3_head_21
 pr3/props pr3_head_12
-pr3/props pr3_flat
 pr3/props pr3_eta
 pr3/subst1 pr3_subst1
 pr3/subst1 pr3_gen_cabbr
diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
index e01515313..ed6ee27e3 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
@@ -82,4 +82,7 @@ elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3/ *
 #W2 #T2 #HW2 #HT2 #H destruct /4 width=5/
 qed-.
 
-(* Basic_1: removed theorems 2: clear_pr3_trans pr3_cflat *)
+(* Basic_1: removed theorems 5:
+   clear_pr3_trans pr3_cflat
+   pr3_iso_appl_bind pr3_iso_appls_appl_bind pr3_iso_appls_bind
+*)
diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
index 47ec400c8..ca3fe09da 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
@@ -75,6 +75,7 @@ theorem cprs_conf: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ➡* T2 →
 theorem cprs_trans: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
 /2 width=3/ qed.
 
+(* Basic_1: was: pr3_flat *)
 lemma cprs_flat: ∀I,L,T1,T2. L ⊢ T1 ➡* T2 → ∀V1,V2. L ⊢ V1 ➡* V2 →
                  L ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
 #I #L #T1 #T2 #HT12 #V1 #V2 #HV12 @(cprs_ind … HV12) -V2 /2 width=1/
@@ -82,6 +83,13 @@ lemma cprs_flat: ∀I,L,T1,T2. L ⊢ T1 ➡* T2 → ∀V1,V2. L ⊢ V1 ➡* V2 
 @(cprs_trans … IHV1) -IHV1 /2 width=1/ 
 qed.
 
+lemma cprs_abbr: ∀L,V1,T1,T2. L. ⓓV1 ⊢ T1 ➡* T2 → ∀V2. L ⊢ V1 ➡* V2 →
+                 L ⊢ ⓓV1. T1 ➡* ⓓV2. T2.
+#L #V1 #T1 #T2 #HT12 #V2 #HV12 @(cprs_ind … HV12) -V2 /2 width=1/
+#V #V2 #_ #HV2 #IHV1
+@(cprs_trans … IHV1) -IHV1 /2 width=1/
+qed.
+
 (* Basic_1: was only: pr3_pr2_pr3_t pr3_wcpr0_t *)
 lemma lcpr_cprs_trans: ∀L1,L2. L1 ⊢ ➡ L2 →
                        ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
index cbbf170f9..6969f7c60 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
@@ -13,41 +13,60 @@
 (**************************************************************************)
 
 include "basic_2/grammar/tstc.ma".
-(*
-include "basic_2/reducibility/cpr_lift.ma".
-include "basic_2/reducibility/lcpr_cpr.ma".
-*)
-include "basic_2/computation/cprs_cprs.ma".
+include "basic_2/computation/cprs_lift.ma".
+include "basic_2/computation/cprs_lcprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
 (* Forward lemmas involving same top term constructor ***********************)
-(*
-lemma cpr_fwd_beta: ∀L,V,W,T,U. L ⊢ ⓐV. ⓛW. T ➡ U →
-                    ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⓓV. T ➡* U.
+
+(* Basic_1: was: pr3_iso_beta *)
+lemma cprs_fwd_beta: ∀L,V,W,T,U. L ⊢ ⓐV. ⓛW. T ➡* U →
+                     ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⓓV. T ➡* U.
 #L #V #W #T #U #H
-elim (cpr_inv_appl1 … H) -H *
-[ #V0 #X #_ #_ #H destruct /2 width=1/
-| #V0 #W0 #T1 #T2 #HV0 #HT12 #H1 #H2 destruct
-  lapply (lcpr_cpr_trans (L. ⓓV) … HT12) -HT12 /2 width=1/ /3 width=1/
-| #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #H destruct
+elim (cprs_inv_appl1 … H) -H *
+[ #V0 #T0 #_ #_ #H destruct /2 width=1/
+| #V0 #W0 #T0 #HV0 #HT0 #HU
+  elim (cprs_inv_abst1 Abbr V … HT0) -HT0 #W1 #T1 #_ #HT1 #H destruct -W1
+  @or_intror -W
+  @(cprs_trans … HU) -U /2 width=1/ (**) (* explicit constructor *)
+| #V1 #V2 #V0 #T1 #_ #_ #HT1 #_
+  elim (cprs_inv_abst1 Abbr V … HT1) -HT1 #W2 #T2 #_ #_ #H destruct
 ]
 qed-.
 
-lemma cpr_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡ U →
-                     ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
-                     L ⊢ ⓓV. ⓐV2. T ➡* U.
+lemma cprs_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡* U →
+                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
+                      L ⊢ ⓓV. ⓐV2. T ➡* U.
 #L #V1 #V #T #U #H #V2 #HV12
-elim (cpr_inv_appl1 … H) -H *
-[ -HV12 #V0 #X #_ #_ #H destruct /2 width=1/
-| -HV12 #V0 #W #T1 #T2 #_ #_ #H destruct
-| #V0 #V3 #W1 #W2 #T1 #T2 #HV10 #HW12 #HT12 #HV03 #H1 #H2 destruct
-  lapply (cpr_lift (L.ⓓW1) … HV12 … HV03 … HV10) -V0 -HV12 /2 width=1/ #HV23
-  lapply (lcpr_cpr_trans (L. ⓓW1) … HT12) -HT12 /2 width=1/ #HT12
-  /4 width=1/
+elim (cprs_inv_appl1 … H) -H *
+[ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1/
+| #V0 #W #T0 #HV10 #HT0 #HU
+  elim (cprs_inv_abbr1 … HT0) -HT0 *
+  [ #V3 #T3 #_ #_ #H destruct
+  | #X #H #HT2
+    elim (lift_inv_bind1 … H) -H #W2 #T2 #HW2 #HT02 #H destruct
+    @or_intror @(cprs_trans … HU) -U (**) (* explicit constructor *)
+    @(cprs_trans … (ⓓV.ⓐV2.ⓛW2.T2)) [ /3 width=1/ ] -T
+    @(cprs_strap2 … (ⓐV1.ⓛW.T0)) [ /5 width=3/ ] -V -V2 -W2 -T2
+    @(cprs_strap2 … (ⓓV1.T0)) [ /3 width=1/ ] -W /2 width=1/
+  ]
+| #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
+  @or_intror @(cprs_trans … HU) -U (**) (* explicit constructor *)
+  elim (cprs_inv_abbr1 … HT0) -HT0 *
+  [ #V5 #T5 #HV5 #HT5 #H destruct
+    lapply (cprs_lift (L.ⓓV) … HV12 … HV13 … HV34) -V1 -V3 /2 width=1/
+    /3 width=1/
+  | #X #H #HT1
+    elim (lift_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
+    lapply (cprs_lift (L.ⓓV0) … HV12 … HV13 … HV34) -V3 /2 width=1/ #HV24
+    @(cprs_trans … (ⓓV.ⓐV2.ⓓV5.T5)) [ /3 width=1/ ] -T
+    @(cprs_strap2 … (ⓐV1.ⓓV0.T0)) [ /5 width=3/ ] -V -V5 -T5
+    @(cprs_strap2 … (ⓓV0.ⓐV2.T0)) [ /3 width=3/ ] -V1 /3 width=9/
+  ]
 ]
 qed-.
-*)
+
 lemma cprs_fwd_tau: ∀L,W,T,U. L ⊢ ⓣW. T ➡* U →
                     ⓣW. T ≃ U ∨ L ⊢ T ➡* U.
 #L #W #T #U #H
diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
index 220f8a648..fdbc9458f 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
@@ -32,7 +32,7 @@ lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T [d, e] ▶* T2 → L ⊢
 /4 width=3/ qed-.
 
 (* Basic_1: was by definition: pr2_free *)
-lemma cpr_pr: ∀T1,T2. T1 ➡ T2 → ∀L. L ⊢ T1 ➡ T2.
+lemma cpr_tpr: ∀T1,T2. T1 ➡ T2 → ∀L. L ⊢ T1 ➡ T2.
 /2 width=3/ qed.
 
 lemma cpr_tpss: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶* T2 → L ⊢ T1 ➡ T2.