Finalized copy sub-machine of the universal turing machine. Some new results

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ltpss.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ltpss.ma
index 879d4418bb5cbed0020aee698faaf79b1a0ce651..34221e4c54ea103ef4d30eb373f2112c685f4b8a 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ltpss.ma
@@ -18,8 +18,8 @@ include "basic_2/reducibility/tpr_tpss.ma".
 
 (* Properties concerning parallel unfold on local environments **************)
 
-lemma ltpr_ltps_conf: ∀L1,K1,d,e. L1 [d, e] ▶ K1 → ∀L2. L1 ➡ L2 →
-                      ∃∃K2. L2 [d, e] ▶* K2 & K1 ➡ K2.
+lemma ltpr_ltpss_conf: ∀L1,K1,d,e. L1 ▶* [d, e] K1 → ∀L2. L1 ➡ L2 →
+                       ∃∃K2. L2 ▶* [d, e] K2 & K1 ➡ K2.
 #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
 [ /2 width=3/
 | #L1 #I #V1 #X #H
@@ -27,19 +27,10 @@ lemma ltpr_ltps_conf: ∀L1,K1,d,e. L1 [d, e] ▶ K1 → ∀L2. L1 ➡ L2 →
 | #L1 #K1 #I #V1 #W1 #e #_ #HVW1 #IHLK1 #X #H
   elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
   elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
-  elim (tpr_tps_ltpr … HV12 … HVW1 … HK12) -V1 /3 width=5/
+  elim (tpr_tpss_ltpr … HK12 … HV12 … HVW1) -V1 /3 width=5/
 | #L1 #K1 #I #V1 #W1 #d #e #_ #HVW1 #IHLK1 #X #H
   elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
   elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
-  elim (tpr_tps_ltpr … HV12 … HVW1 … HK12) -V1 /3 width=5/
+  elim (tpr_tpss_ltpr … HK12 … HV12 … HVW1) -V1 /3 width=5/
 ]
 qed.
-
-lemma ltpr_ltpss_conf: ∀L1,K1,d,e. L1 [d, e] ▶* K1 → ∀L2. L1 ➡ L2 →
-                       ∃∃K2. L2 [d, e] ▶* K2 & K1 ➡ K2.
-#L1 #K1 #d #e #H @(ltpss_ind … H) -K1 /2 width=3/
-#K #K1 #_ #HK1 #IHK #L2 #HL12
-elim (IHK … HL12) -L1 #K2 #HLK2 #HK2
-elim (ltpr_ltps_conf … HK1 … HK2) -K #K #HK2 #HK1
-lapply (ltpss_trans_eq … HLK2 HK2) -K2 /2 width=3/
-qed.