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[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 958fcab3bc781053975b060c8f5cf558b8dfb4a0..1706ae98ea926422c2355c0bcc9f71977bf34c0c 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] L2 →
+                            ∀V1,V2. ⦃G,L2⦄ ⊢ V1 ➡*[h] V2 →
+                            ∀I. ⦃G,L1.ⓑ{I}V1⦄ ⊢ ➡*[h] 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] T1 →
+                                 ∀L1. ⦃G,L0⦄ ⊢ ➡*[h] L1 →
+                                 ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] 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] T1 →
+                                ∀L1. ⦃G,L0⦄ ⊢ ➡*[h] L1 →
+                                ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] 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] T1 →
+                                 ∀L1. ⦃G,L0⦄ ⊢ ➡*[h] L1 →
+                                 ∃∃T. ⦃G,L0⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] 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] T1 →
+                                ∀L1. ⦃G,L0⦄ ⊢ ➡*[h] L1 →
+                                ∃∃T. ⦃G,L0⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] T.
 /3 width=3 by lprs_cprs_conf_sn, cpm_cpms/ qed-.