- we set up the support for the "bt-reduction" of Automath literature

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
index 12cd0791f0420257af63ad6f10512818c237332e..ae0c1ae627ecc8cf4e95ba20bce361f79d7a155e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/reducibility/cpr.ma".
+include "basic_2/reducibility/cnf.ma".
+include "basic_2/computation/tprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
@@ -28,12 +29,16 @@ interpretation "context-sensitive parallel computation (term)"
 lemma cprs_ind: ∀L,T1. ∀R:predicate term. R T1 →
                 (∀T,T2. L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → R T → R T2) →
                 ∀T2. L ⊢ T1 ➡* T2 → R T2.
-#L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
+#L #T1 #R #HT1 #IHT1 #T2 #HT12
+@(TC_star_ind … HT1 IHT1 … HT12) //
 qed-.
 
-axiom cprs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
+lemma cprs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
                    (∀T1,T. L ⊢ T1 ➡ T → L ⊢ T ➡* T2 → R T → R T1) →
                    ∀T1. L ⊢ T1 ➡* T2 → R T1.
+#L #T2 #R #HT2 #IHT2 #T1 #HT12
+@(TC_star_ind_dx … HT2 IHT2 … HT12) //
+qed-.
 
 (* Basic properties *********************************************************)
 
@@ -51,11 +56,12 @@ lemma cprs_strap2: ∀L,T1,T,T2.
 /2 width=3/ qed.
 
 (* Note: it does not hold replacing |L1| with |L2| *)
-lemma cprs_lsubs_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡* T2 →
-                       ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡* T2.
+lemma cprs_lsubs_trans: ∀L1,T1,T2. L1 ⊢ T1 ➡* T2 →
+                        ∀L2. L2 ≼ [0, |L1|] L1 → L2 ⊢ T1 ➡* T2.
 /3 width=3/
 qed.
 
+(* Basic_1: was only: pr3_thin_dx *)
 lemma cprs_flat_dx: ∀I,L,V1,V2. L ⊢ V1 ➡ V2 → ∀T1,T2. L ⊢ T1 ➡* T2 →
                     L ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
 #I #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cprs_ind … HT12) -T2 /3 width=1/
@@ -63,6 +69,11 @@ lemma cprs_flat_dx: ∀I,L,V1,V2. L ⊢ V1 ➡ V2 → ∀T1,T2. L ⊢ T1 ➡* T2
 @(cprs_strap1 … IHT2) -IHT2 /2 width=1/
 qed.
 
+(* Basic_1: was: pr3_pr1 *)
+lemma tprs_cprs: ∀T1,T2. T1 ➡* T2 → ∀L. L ⊢ T1 ➡* T2.
+#T1 #T2 #H @(tprs_ind … H) -T2 /2 width=1/ /3 width=3/
+qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: was: pr3_gen_sort *)
@@ -73,8 +84,8 @@ lemma cprs_inv_sort1: ∀L,U2,k. L ⊢ ⋆k ➡* U2 → U2 = ⋆k.
 qed-.
 
 (* Basic_1: was: pr3_gen_cast *)
-lemma cprs_inv_cast1: â\88\80L,W1,T1,U2. L â\8a¢ â\93£W1.T1 ➡* U2 → L ⊢ T1 ➡* U2 ∨
-                      â\88\83â\88\83W2,T2. L â\8a¢ W1 â\9e¡* W2 & L â\8a¢ T1 â\9e¡* T2 & U2 = â\93£W2.T2.
+lemma cprs_inv_cast1: â\88\80L,W1,T1,U2. L â\8a¢ â\93\9dW1.T1 ➡* U2 → L ⊢ T1 ➡* U2 ∨
+                      â\88\83â\88\83W2,T2. L â\8a¢ W1 â\9e¡* W2 & L â\8a¢ T1 â\9e¡* T2 & U2 = â\93\9dW2.T2.
 #L #W1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
 #U2 #U #_ #HU2 * /3 width=3/ *
 #W #T #HW1 #HT1 #H destruct
@@ -82,4 +93,18 @@ elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3/ *
 #W2 #T2 #HW2 #HT2 #H destruct /4 width=5/
 qed-.
 
-(* Basic_1: removed theorems 2: clear_pr3_trans pr3_cflat *)
+(* Basic_1: was: nf2_pr3_unfold *)
+lemma cprs_inv_cnf1: ∀L,T,U. L ⊢ T ➡* U → L ⊢ 𝐍⦃T⦄ → T = U.
+#L #T #U #H @(cprs_ind_dx … H) -T //
+#T0 #T #H1T0 #_ #IHT #H2T0
+lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1/
+qed-.
+
+lemma tprs_inv_cnf1: ∀T,U. T ➡* U → ⋆ ⊢ 𝐍⦃T⦄ → T = U.
+/3 width=3 by tprs_cprs, cprs_inv_cnf1/ qed-.
+
+(* Basic_1: removed theorems 10:
+   clear_pr3_trans pr3_cflat pr3_gen_bind
+   pr3_head_1 pr3_head_2 pr3_head_21 pr3_head_12
+   pr3_iso_appl_bind pr3_iso_appls_appl_bind pr3_iso_appls_bind
+*)