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

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
index 4b65a08df3048224bb532e8e4ca153dcb462a24a..5a4c2bc3421c5da738b15ec6e51a91379dd72471 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
@@ -20,6 +20,21 @@ include "basic_2/computation/cprs_tstc.ma".
 
 (* Vector form of forward lemmas involving same top term constructor ********)
 
+(* Basic_1: was just: nf2_iso_appls_lref *)
+lemma cprs_fwd_cnf_vector: ∀L,T.  𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ → ∀Vs,U. L ⊢ ⒶVs.T ➡* U → ⒶVs.T ≃ U.
+#L #T #H1T #H2T #Vs elim Vs -Vs [ @(cprs_fwd_cnf … H2T) ] (**) (* /2 width=3 by cprs_fwd_cnf/ does not work *)
+#V #Vs #IHVs #U #H
+elim (cprs_inv_appl1 … H) -H *
+[ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
+| #V0 #W0 #T0 #HV0 #HT0 #HU
+  lapply (IHVs … HT0) -IHVs -HT0 #HT0
+  elim (tstc_inv_bind_appls_simple … HT0 ?) //
+| #V1 #V2 #V0 #T0 #HV1 #HV12 #HT0 #HU
+  lapply (IHVs … HT0) -IHVs -HT0 #HT0
+  elim (tstc_inv_bind_appls_simple … HT0 ?) //
+]
+qed-.
+
 (* Basic_1: was: pr3_iso_appls_beta *)
 lemma cprs_fwd_beta_vector: ∀L,Vs,V,W,T,U. L ⊢ ⒶVs. ⓐV. ⓛW. T ➡* U →
                             ⒶVs. ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⒶVs. ⓓV. T ➡* U.
@@ -44,6 +59,31 @@ elim (cprs_inv_appl1 … H) -H *
 ]
 qed-.
 
+lemma cprs_fwd_delta_vector: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
+                             ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
+                             ∀Vs,U. L ⊢ ⒶVs.#i ➡* U →
+                             ⒶVs.#i ≃ U ∨ L ⊢ ⒶVs.V2 ➡* U.
+#L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs /2 width=4 by cprs_fwd_delta/
+#V #Vs #IHVs #U #H -K -V1
+elim (cprs_inv_appl1 … H) -H *
+[ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
+| #V0 #W0 #T0 #HV0 #HT0 #HU
+  elim (IHVs … HT0) -IHVs -HT0 #HT0
+  [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
+  | @or_intror -i (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=1/
+  ]
+| #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
+  elim (IHVs … HT0) -IHVs -HT0 #HT0
+  [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
+  | @or_intror -i (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV0.ⓓV3.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=3/
+  ]
+]
+qed-.
+
 (* Basic_1: was: pr3_iso_appls_abbr *)
 lemma cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
                              ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
@@ -94,8 +134,8 @@ elim (cprs_inv_appl1 … H) -H *
 qed-.
 
 (* Basic_1: was: pr3_iso_appls_cast *)
-lemma cprs_fwd_tau_vector: â\88\80L,Vs,W,T,U. L â\8a¢ â\92¶Vs. â\93£W. T ➡* U →
-                           â\92¶Vs. â\93£W. T ≃ U ∨ L ⊢ ⒶVs. T ➡* U.
+lemma cprs_fwd_tau_vector: â\88\80L,Vs,W,T,U. L â\8a¢ â\92¶Vs. â\93\9dW. T ➡* U →
+                           â\92¶Vs. â\93\9dW. T ≃ U ∨ L ⊢ ⒶVs. T ➡* U.
 #L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_tau/
 #V #Vs #IHVs #W #T #U #H
 elim (cprs_inv_appl1 … H) -H *