From 58ddc56896384e0a1e8a7d331aae9eded8510c70 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Fri, 11 May 2018 16:40:36 +0200
Subject: [PATCH] update in basic_2

+ cprs.ma completely ported
---
 .../basic_2/rt_computation/cpms.ma            | 54 ++++++++++++++++
 .../basic_2/rt_computation/cprs.ma            | 61 ++++++-------------
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  8 ++-
 3 files changed, 78 insertions(+), 45 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
index edb931591..8c73990c8 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
@@ -71,6 +71,60 @@ lemma cpms_bind_dx (n) (h) (G) (L):
 #n #h #G #L #V1 #V2 #HV12 #I #T1 #T2 #H #a @(cpms_ind_sn … H) -T1
 /3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind/ qed.
 
+lemma cpms_appl_dx (n) (h) (G) (L):
+                   ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
+                   ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 →
+                   ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[n, h] ⓐV2.T2.
+#n #h #G #L #V1 #V2 #HV12 #T1 #T2 #H @(cpms_ind_sn … H) -T1
+/3 width=3 by cpms_step_sn, cpm_cpms, cpm_appl/
+qed.
+
+(* Basic_2A1: uses: cprs_zeta *)
+lemma cpms_zeta (n) (h) (G) (L):
+                ∀T2,T. ⬆*[1] T2 ≘ T →
+                ∀V,T1. ⦃G, L.ⓓV⦄ ⊢ T1 ➡*[n, h] T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡*[n, h] T2.
+#n #h #G #L #T2 #T #HT2 #V #T1 #H @(cpms_ind_sn … H) -T1
+/3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind, cpm_zeta/
+qed.
+
+(* Basic_2A1: uses: cprs_eps *)
+lemma cpms_eps (n) (h) (G) (L):
+               ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 →
+               ∀V. ⦃G, L⦄ ⊢ ⓝV.T1 ➡*[n, h] T2.
+#n #h #G #L #T1 #T2 #H @(cpms_ind_sn … H) -T1
+/3 width=3 by cpms_step_sn, cpm_cpms, cpm_eps/
+qed.
+
+(* Basic_2A1: uses: cprs_beta_dx *)
+lemma cpms_beta_dx (n) (h) (G) (L):
+                   ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
+                   ∀W1,W2. ⦃G, L⦄ ⊢ W1 ➡[h] W2 →
+                   ∀T1,T2. ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[n, h] T2 →
+                   ∀p. ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ➡*[n, h] ⓓ{p}ⓝW2.V2.T2.
+#n #h #G #L #V1 #V2 #HV12 #W1 #W2 #HW12 #T1 #T2 #H @(cpms_ind_dx … H) -T2
+/4 width=7 by cpms_step_dx, cpm_cpms, cpms_bind_dx, cpms_appl_dx, cpm_beta/
+qed.
+
+(* Basic_2A1: uses: cprs_theta_dx *)
+lemma cpms_theta_dx (n) (h) (G) (L):
+                    ∀V1,V. ⦃G, L⦄ ⊢ V1 ➡[h] V →
+                    ∀V2. ⬆*[1] V ≘ V2 →
+                    ∀W1,W2. ⦃G, L⦄ ⊢ W1 ➡[h] W2 →
+                    ∀T1,T2. ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[n, h] T2 →
+                    ∀p. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡*[n, h] ⓓ{p}W2.ⓐV2.T2.
+#n #h #G #L #V1 #V #HV1 #V2 #HV2 #W1 #W2 #HW12 #T1 #T2 #H @(cpms_ind_dx … H) -T2
+/4 width=9 by cpms_step_dx, cpm_cpms, cpms_bind_dx, cpms_appl_dx, cpm_theta/
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma cpms_inv_sort1 (n) (h) (G) (L): ∀X2,s. ⦃G, L⦄ ⊢ ⋆s ➡*[n, h] X2 → X2 = ⋆(((next h)^n) s).
+#n #h #G #L #X2 #s #H @(cpms_ind_dx … H) -X2 //
+#n1 #n2 #X #X2 #_ #IH #HX2 destruct
+elim (cpm_inv_sort1 … HX2) -HX2 * // #H1 #H2 destruct
+/2 width=3 by refl, trans_eq/
+qed-.
+
 (* Basic properties with r-transition ***************************************)
 
 (* Basic_1: was: pr3_refl *)
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
index af0618bc5..e26838e19 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
@@ -68,57 +68,34 @@ lemma cprs_flat_dx (h) (I) (G) (L):
 #h #I #G #L #V1 #V2 #HV12 #T1 #T2 #H @(cprs_ind_sn … H) -T1
 /3 width=3 by cprs_step_sn, cpm_cpms, cpr_flat/
 qed.
-(*
-lemma cprs_flat_sn: ∀I,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h] V2 →
-                    ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡*[h] ⓕ{I} V2. T2.
-#I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind … H) -V2
-/3 width=3 by cprs_strap1, cpr_cprs, cpr_pair_sn, cpr_flat/
-qed.
-
-lemma cprs_zeta: ∀G,L,V,T1,T,T2. ⬆[0, 1] T2 ≘ T →
-                 ⦃G, L.ⓓV⦄ ⊢ T1 ➡*[h] T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡*[h] T2.
-#G #L #V #T1 #T #T2 #HT2 #H @(cprs_ind_dx … H) -T1
-/3 width=3 by cprs_strap2, cpr_cprs, cpr_bind, cpr_zeta/
-qed.
 
-lemma cprs_eps: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → ∀V. ⦃G, L⦄ ⊢ ⓝV.T1 ➡*[h] T2.
-#G #L #T1 #T2 #H @(cprs_ind … H) -T2
-/3 width=3 by cprs_strap1, cpr_cprs, cpr_eps/
-qed.
-
-lemma cprs_beta_dx: ∀a,G,L,V1,V2,W1,W2,T1,T2.
-                    ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h] T2 →
-                    ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h] ⓓ{a}ⓝW2.V2.T2.
-#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 * -T2
-/4 width=7 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_beta/
-qed.
-
-lemma cprs_theta_dx: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
-                     ⦃G, L⦄ ⊢ V1 ➡[h] V → ⬆[0, 1] V ≘ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h] T2 →
-                     ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h] ⓓ{a}W2.ⓐV2.T2.
-#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
-/4 width=9 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_theta/
+lemma cprs_flat_sn (h) (I) (G) (L):
+                   ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h] V2 →
+                   ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡*[h] ⓕ{I} V2. T2.
+#h #I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind_sn … H) -V1
+/3 width=3 by cprs_step_sn, cpm_cpms, cpr_flat/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: was: pr3_gen_sort *)
-lemma cprs_inv_sort1: ∀G,L,U2,s. ⦃G, L⦄ ⊢ ⋆s ➡*[h] U2 → U2 = ⋆s.
-#G #L #U2 #s #H @(cprs_ind … H) -U2 //
-#U2 #U #_ #HU2 #IHU2 destruct
->(cpr_inv_sort1 … HU2) -HU2 //
-qed-.
+lemma cprs_inv_sort1 (h) (G) (L): ∀X2,s. ⦃G, L⦄ ⊢ ⋆s ➡*[h] X2 → X2 = ⋆s.
+/2 width=4 by cpms_inv_sort1/ qed-.
 
 (* Basic_1: was: pr3_gen_cast *)
-lemma cprs_inv_cast1: ∀G,L,W1,T1,U2. ⦃G, L⦄ ⊢ ⓝW1.T1 ➡*[h] U2 → ⦃G, L⦄ ⊢ T1 ➡*[h] U2 ∨
-                      ∃∃W2,T2. ⦃G, L⦄ ⊢ W1 ➡*[h] W2 & ⦃G, L⦄ ⊢ T1 ➡*[h] T2 & U2 = ⓝW2.T2.
-#G #L #W1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_intror/
-#U2 #U #_ #HU2 * /3 width=3 by cprs_strap1, or_introl/ *
-#W #T #HW1 #HT1 #H destruct
-elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3 by cprs_strap1, or_introl/ *
-#W2 #T2 #HW2 #HT2 #H destruct /4 width=5 by cprs_strap1, ex3_2_intro, or_intror/
+lemma cprs_inv_cast1 (h) (G) (L): ∀W1,T1,X2. ⦃G, L⦄ ⊢ ⓝW1.T1 ➡*[h] X2 →
+                                  ∨∨ ⦃G, L⦄ ⊢ T1 ➡*[h] X2
+                                   | ∃∃W2,T2. ⦃G, L⦄ ⊢ W1 ➡*[h] W2 & ⦃G, L⦄ ⊢ T1 ➡*[h] T2 & X2 = ⓝW2.T2.
+#h #G #L #W1 #T1 #X2 #H @(cprs_ind_dx … H) -X2
+[ /3 width=5 by ex3_2_intro, or_intror/
+| #X #X2 #_ #HX2 * /3 width=3 by cprs_step_dx, or_introl/ *
+  #W #T #HW1 #HT1 #H destruct
+  elim (cpr_inv_cast1 … HX2) -HX2 /3 width=3 by cprs_step_dx, or_introl/ *
+  #W2 #T2 #HW2 #HT2 #H destruct
+  /4 width=5 by cprs_step_dx, ex3_2_intro, or_intror/
+]
 qed-.
-*)
+
 (* Basic_1: removed theorems 13:
    pr1_head_1 pr1_head_2 pr1_comp
    clear_pr3_trans pr3_cflat pr3_gen_bind
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index ff9b21627..eb146dd0b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -78,12 +78,14 @@ table {
              [ [ "" ] "scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )" "scpds_lift" + "scpds_aaa" + "scpds_scpds" * ]
           }
         ]
-        [ { "context-sensitive computation" * } {
+*)        
+        [ { "context-sensitive parallel r-computation" * } {
+(*
              [ [ "" ] "lprs ( ⦃?,?⦄ ⊢ ➡* ? )" "lprs_drop" + "lprs_cprs" + "lprs_lprs" * ]
-             [ [ "" ] "cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
+*)
+             [ [ "for terms" ] "cprs" + "( ⦃?,?⦄ ⊢ ? ➡*[?] ?)" (* "cprs_lift" + "cprs_cprs" *) * ]
           }
         ]
-*)
         [ { "t-bound context-sensitive parallel rt-computation" * } {
              [ [ "for terms" ] "cpms" + "( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" * ]
           }
-- 
2.39.2