update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cprs.ma

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 e26838e192695bf583055818606e1783c83b5c64..4b221d5a4337107714d10449aa983a6c856c776e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
@@ -15,16 +15,16 @@
 include "basic_2/rt_transition/cpr.ma".
 include "basic_2/rt_computation/cpms.ma".
 
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION FOR TERMS *************************)
+(* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
 
 (* Basic eliminators ********************************************************)
 
 (* Basic_2A1: was: cprs_ind_dx *)
-lemma cprs_ind_sn (h) (G) (L) (T2) (R:predicate …):
-                  R T2 →
-                  (â\88\80T1,T. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h] T â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡*[h] T2 â\86\92 R T â\86\92 R T1) →
-                  â\88\80T1. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T2 â\86\92 R T1.
-#h #G #L #T2 #R #IH1 #IH2 #T1
+lemma cprs_ind_sn (h) (G) (L) (T2) (Q:predicate …):
+                  Q T2 →
+                  (â\88\80T1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T â\86\92 â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h] T2 â\86\92 Q T â\86\92 Q T1) →
+                  â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T2 â\86\92 Q T1.
+#h #G #L #T2 #Q #IH1 #IH2 #T1
 @(insert_eq_0 … 0) #n #H
 @(cpms_ind_sn … H) -n -T1 //
 #n1 #n2 #T1 #T #HT1 #HT2 #IH #H
@@ -33,11 +33,11 @@ elim (plus_inv_O3 n1 n2) // -H #H1 #H2 destruct
 qed-.
 
 (* Basic_2A1: was: cprs_ind *)
-lemma cprs_ind_dx (h) (G) (L) (T1) (R:predicate …):
-                  R T1 →
-                  (â\88\80T,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡[h] T2 â\86\92 R T â\86\92 R T2) →
-                  â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T2 â\86\92 R T2.
-#h #G #L #T1 #R #IH1 #IH2 #T2
+lemma cprs_ind_dx (h) (G) (L) (T1) (Q:predicate …):
+                  Q T1 →
+                  (â\88\80T,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T â\86\92 â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h] T2 â\86\92 Q T â\86\92 Q T2) →
+                  â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T2 â\86\92 Q T2.
+#h #G #L #T1 #Q #IH1 #IH2 #T2
 @(insert_eq_0 … 0) #n #H
 @(cpms_ind_dx … H) -n -T2 //
 #n1 #n2 #T #T2 #HT1 #IH #HT2 #H
@@ -50,28 +50,28 @@ qed-.
 (* Basic_1: was: pr3_step *)
 (* Basic_2A1: was: cprs_strap2 *)
 lemma cprs_step_sn (h) (G) (L):
-                   â\88\80T1,T. â¦\83G, Lâ¦\84 ⊢ T1 ➡[h] T →
-                   â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡*[h] T2 â\86\92 â¦\83G, Lâ¦\84 ⊢ T1 ➡*[h] T2.
+                   â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡[h] T →
+                   â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T2.
 /2 width=3 by cpms_step_sn/ qed-.
 
 (* Basic_2A1: was: cprs_strap1 *)
 lemma cprs_step_dx (h) (G) (L):
-                   â\88\80T1,T. â¦\83G, Lâ¦\84 ⊢ T1 ➡*[h] T →
-                   â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡[h] T2 â\86\92 â¦\83G, Lâ¦\84 ⊢ T1 ➡*[h] T2.
+                   â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T →
+                   â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T2.
 /2 width=3 by cpms_step_dx/ qed-.
 
 (* Basic_1: was only: pr3_thin_dx *)
 lemma cprs_flat_dx (h) (I) (G) (L):
-                   â\88\80V1,V2. â¦\83G, Lâ¦\84 ⊢ V1 ➡[h] V2 →
-                   â\88\80T1,T2. â¦\83G, Lâ¦\84 ⊢ T1 ➡*[h] T2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â\9e¡*[h] â\93\95{I}V2.T2.
+                   â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+                   â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T2 →
+                   â\9dªG,Lâ\9d« â\8a¢ â\93\95[I]V1.T1 â\9e¡*[h] â\93\95[I]V2.T2.
 #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 (h) (I) (G) (L):
-                   â\88\80T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\86\92 â\88\80V1,V2. â¦\83G, Lâ¦\84 ⊢ V1 ➡*[h] V2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ â\93\95{I} V1. T1 â\9e¡*[h] â\93\95{I} V2. T2.
+                   â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\86\92 â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡*[h] V2 →
+                   â\9dªG,Lâ\9d« â\8a¢ â\93\95[I] V1. T1 â\9e¡*[h] â\93\95[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.
@@ -79,20 +79,18 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: was: pr3_gen_sort *)
-lemma cprs_inv_sort1 (h) (G) (L): â\88\80X2,s. â¦\83G, Lâ¦\84 ⊢ ⋆s ➡*[h] X2 → X2 = ⋆s.
+lemma cprs_inv_sort1 (h) (G) (L): â\88\80X2,s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡*[h] X2 → X2 = ⋆s.
 /2 width=4 by cpms_inv_sort1/ qed-.
 
 (* Basic_1: was: pr3_gen_cast *)
-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/
+lemma cprs_inv_cast1 (h) (G) (L): ∀W1,T1,X2. ❪G,L❫ ⊢ ⓝW1.T1 ➡*[h] X2 →
+                                  ∨∨ ∃∃W2,T2. ❪G,L❫ ⊢ W1 ➡*[h] W2 & ❪G,L❫ ⊢ T1 ➡*[h] T2 & X2 = ⓝW2.T2
+                                   | ❪G,L❫ ⊢ T1 ➡*[h] X2.
+#h #G #L #W1 #T1 #X2 #H
+elim (cpms_inv_cast1 … H) -H
+[ /2 width=1 by or_introl/
+| /2 width=1 by or_intror/
+| * #m #_ #H destruct
 ]
 qed-.