update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_cprs.ma
index fafeabe1e754ff81895f356f4e0817d857bb1c1b..5dc4727467c77ddd7e88949fa57a80696b80f1e0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_cprs.ma
@@ -20,16 +20,16 @@ include "basic_2/rt_computation/lprs_cpms.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: lprs_pair2 *)
-lemma lprs_pair_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h] L2 →
-                            ∀V1,V2. ❪G,L2❫ ⊢ V1 ➡*[h] V2 →
-                            ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ➡*[h] L2.ⓑ[I]V2.
+lemma lprs_pair_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 →
+                            ∀V1,V2. ❪G,L2❫ ⊢ V1 ➡*[h,0] V2 →
+                            ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ➡*[h,0] L2.ⓑ[I]V2.
 /3 width=3 by lprs_pair, lprs_cpms_trans/ qed.
 
 (* Properties on context-sensitive parallel r-computation for terms *********)
 
-lemma lprs_cprs_conf_dx (h) (G): ∀L0.∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡*[h] T1 →
-                                 ∀L1. ❪G,L0❫ ⊢ ➡*[h] L1 →
-                                 ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h] T & ❪G,L1❫ ⊢ T0 ➡*[h] T.
+lemma lprs_cprs_conf_dx (h) (G): ∀L0.∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡*[h,0] T1 →
+                                 ∀L1. ❪G,L0❫ ⊢ ➡*[h,0] L1 →
+                                 ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
 #h #G #L0 #T0 #T1 #HT01 #L1 #H
 @(lprs_ind_dx … H) -L1 /2 width=3 by ex2_intro/
 #L #L1 #_ #HL1 * #T #HT1 #HT0 -L0
@@ -39,21 +39,21 @@ elim (cprs_conf … HT2 … HT3) -T
 /3 width=5 by cprs_trans, ex2_intro/
 qed-.
 
-lemma lprs_cpr_conf_dx (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡[h] T1 →
-                                ∀L1. ❪G,L0❫ ⊢ ➡*[h] L1 →
-                                ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h] T & ❪G,L1❫ ⊢ T0 ➡*[h] T.
+lemma lprs_cpr_conf_dx (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡[h,0] T1 →
+                                ∀L1. ❪G,L0❫ ⊢ ➡*[h,0] L1 →
+                                ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
 /3 width=3 by lprs_cprs_conf_dx, cpm_cpms/ qed-.
 
 (* Note: this can be proved on its own using lprs_ind_sn *)
-lemma lprs_cprs_conf_sn (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡*[h] T1 →
-                                 ∀L1. ❪G,L0❫ ⊢ ➡*[h] L1 →
-                                 ∃∃T. ❪G,L0❫ ⊢ T1 ➡*[h] T & ❪G,L1❫ ⊢ T0 ➡*[h] T.
+lemma lprs_cprs_conf_sn (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡*[h,0] T1 →
+                                 ∀L1. ❪G,L0❫ ⊢ ➡*[h,0] L1 →
+                                 ∃∃T. ❪G,L0❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
 #h #G #L0 #T0 #T1 #HT01 #L1 #HL01
 elim (lprs_cprs_conf_dx … HT01 … HL01) -HT01
 /3 width=3 by lprs_cpms_trans, ex2_intro/
 qed-.
 
-lemma lprs_cpr_conf_sn (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡[h] T1 →
-                                ∀L1. ❪G,L0❫ ⊢ ➡*[h] L1 →
-                                ∃∃T. ❪G,L0❫ ⊢ T1 ➡*[h] T & ❪G,L1❫ ⊢ T0 ➡*[h] T.
+lemma lprs_cpr_conf_sn (h) (G): ∀L0. ∀T0,T1:term. ❪G,L0❫ ⊢ T0 ➡[h,0] T1 →
+                                ∀L1. ❪G,L0❫ ⊢ ➡*[h,0] L1 →
+                                ∃∃T. ❪G,L0❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
 /3 width=3 by lprs_cprs_conf_sn, cpm_cpms/ qed-.