update in static_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cnuw_cnuw.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma
@@ -0,0 +1,51 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/rt_computation/cnuw.ma".
+include "basic_2/rt_computation/cprs_tweq.ma".
+include "basic_2/rt_computation/lprs_cpms.ma".
+
+(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma cnuw_inv_abbr_pos (h) (G) (L):
+      ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
+#h #G #L #V #T1 #H
+elim (cprs_abbr_pos_twneq h G L V T1) #T2 #HT12 #HnT12
+/3 width=2 by/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cnuw_abbr_neg (h) (G) (L): ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
+#h #G #L #V1 #T1 #n #X #H
+elim (cpms_inv_abbr_sn_dx … H) -H *
+[ #V2 #T2 #_ #_ #H destruct /1 width=1 by tweq_abbr_neg/
+| #X1 #_ #_ #H destruct
+]
+qed.
+
+lemma cnuw_abst (h) (p) (G) (L): ∀W,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓛ{p}W.T.
+#h #p #G #L #W1 #T1 #n #X #H
+elim (cpms_inv_abst_sn … H) -H #W2 #T2 #_ #_ #H destruct
+/1 width=1 by tweq_abst/
+qed.
+
+lemma cnuw_cpms_trans (h) (n) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T1 →
+      ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T2.
+#h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
+/4 width=5 by cpms_trans, tweq_canc_sn/
+qed-.