- predefined_virtuals: an addition

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / cpr.ma

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 34ad5d844841885bdf538b195c172e504d121c95..072d951babf91b355a7005f522192e6f60afb2b2 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
@@ -20,7 +20,7 @@ include "basic_2/reducibility/tpr.ma".
 
 (* Basic_1: includes: pr2_delta1 *)
 definition cpr: lenv → relation term ≝
-   λL,T1,T2. ∃∃T. T1 ➡ T & L ⊢ T [0, |L|] ▶* T2.
+   λL,T1,T2. ∃∃T. T1 ➡ T & L ⊢ T ▶* [0, |L|] T2.
 
 interpretation
    "context-sensitive parallel reduction (term)"
@@ -28,14 +28,14 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T [d, e] ▶* T2 → L ⊢ T1 ➡ T2.
+lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
 /4 width=3/ qed-.
 
 (* Basic_1: was by definition: pr2_free *)
 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.
+lemma cpr_tpss: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
 /3 width=5/ qed.
 
 lemma cpr_refl: ∀L,T. L ⊢ T ➡ T.
@@ -49,16 +49,16 @@ lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
 qed.
 
 lemma cpr_cast: ∀L,V,T1,T2.
-                L â\8a¢ T1 â\9e¡ T2 â\86\92 L â\8a¢ â\93£V. T1 ➡ T2.
+                L â\8a¢ T1 â\9e¡ T2 â\86\92 L â\8a¢ â\93\9dV. T1 ➡ T2.
 #L #V #T1 #T2 * /3 width=3/
 qed.
 
 (* Note: it does not hold replacing |L1| with |L2| *)
 (* Basic_1: was only: pr2_change *)
-lemma cpr_lsubs_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
-                      ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡ T2.
+lemma cpr_lsubs_trans: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
+                       ∀L2. L2 ≼ [0, |L1|] L1 → L2 ⊢ T1 ➡ T2.
 #L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12 
-lapply (tpss_lsubs_conf … HT2 … HL12) -HT2 -HL12 /3 width=4/
+lapply (tpss_lsubs_trans … HT2 … HL12) -HT2 -HL12 /3 width=4/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -78,7 +78,7 @@ qed-.
 
 (* Basic_1: was pr2_gen_abbr *)
 lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
-                     (∃∃V,V2,T2. V1 ➡ V & L ⊢ V [O, |L|] ▶* V2 &
+                     (∃∃V,V2,T2. V1 ➡ V & L ⊢ V ▶* [O, |L|] V2 &
                                  L. ⓓV ⊢ T1 ➡ T2 &
                                  U2 = ⓓV2. T2
                       ) ∨
@@ -87,9 +87,9 @@ lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
 elim (tpr_inv_abbr1 … H1) -H1 *
 [ #V #T0 #T #HV1 #HT10 #HT0 #H destruct
   elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
-  lapply (tps_lsubs_conf … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
+  lapply (tps_lsubs_trans … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
   lapply (tps_weak_all … HT0) -HT0 #HT0
-  lapply (tpss_lsubs_conf … HT2 (L. ⓓV) ?) -HT2 /2 width=1/ #HT2
+  lapply (tpss_lsubs_trans … HT2 (L. ⓓV) ?) -HT2 /2 width=1/ #HT2
   lapply (tpss_weak_all … HT2) -HT2 #HT2
   lapply (tpss_strap … HT0 HT2) -T /4 width=7/
 | /4 width=5/
@@ -97,9 +97,9 @@ elim (tpr_inv_abbr1 … H1) -H1 *
 qed-.
 
 (* Basic_1: was: pr2_gen_cast *)
-lemma cpr_inv_cast1: â\88\80L,V1,T1,U2. L â\8a¢ â\93£V1. T1 ➡ U2 → (
+lemma cpr_inv_cast1: â\88\80L,V1,T1,U2. L â\8a¢ â\93\9dV1. T1 ➡ U2 → (
                         ∃∃V2,T2. L ⊢ V1 ➡ V2 & L ⊢ T1 ➡ T2 &
-                                 U2 = â\93£V2. T2
+                                 U2 = â\93\9dV2. T2
                      ) ∨ L ⊢ T1 ➡ U2.
 #L #V1 #T1 #U2 * #X #H #HU2
 elim (tpr_inv_cast1 … H) -H /3 width=3/