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

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / cprs_tstc.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
index 6969f7c60b5bddd70caf147ab0ee7f9b613744a9..eb59c5f84a44f4e11dbd6b059edb13e54cd485ae 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
@@ -20,6 +20,11 @@ include "basic_2/computation/cprs_lcprs.ma".
 
 (* Forward lemmas involving same top term constructor ***********************)
 
+lemma cprs_fwd_cnf: ∀L,T. L ⊢ 𝐍⦃T⦄ → ∀U. L ⊢ T ➡* U → T ≃ U.
+#L #T #HT #U #H
+>(cprs_inv_cnf1 … H HT) -L -T //
+qed-.
+
 (* Basic_1: was: pr3_iso_beta *)
 lemma cprs_fwd_beta: ∀L,V,W,T,U. L ⊢ ⓐV. ⓛW. T ➡* U →
                      ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⓓV. T ➡* U.
@@ -35,6 +40,18 @@ elim (cprs_inv_appl1 … H) -H *
 ]
 qed-.
 
+(* Note: probably this is an inversion lemma *)
+lemma cprs_fwd_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
+                      ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
+                      ∀U. L ⊢ #i ➡* U →
+                      #i ≃ U ∨ L ⊢ V2 ➡* U.
+#L #K #V1 #i #HLK #V2 #HV12 #U #H
+elim (cprs_inv_lref1 … H) -H /2 width=1/
+* #K0 #V0 #U0 #HLK0 #HVU0 #HU0 #_
+lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct
+lapply (ldrop_fwd_ldrop2 … HLK) -HLK /3 width=9/
+qed-.
+
 lemma cprs_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡* U →
                       ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
                       L ⊢ ⓓV. ⓐV2. T ➡* U.
@@ -67,8 +84,8 @@ elim (cprs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cprs_fwd_tau: â\88\80L,W,T,U. L â\8a¢ â\93£W. T ➡* U →
-                    â\93£W. T ≃ U ∨ L ⊢ T ➡* U.
+lemma cprs_fwd_tau: â\88\80L,W,T,U. L â\8a¢ â\93\9dW. T ➡* U →
+                    â\93\9dW. T ≃ U ∨ L ⊢ T ➡* U.
 #L #W #T #U #H
 elim (cprs_inv_cast1 … H) -H /2 width=1/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1/