update in static_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_drops.ma
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/relocation/lifts_tweq.ma".
+include "basic_2/rt_computation/cpms_drops.ma".
+include "basic_2/rt_computation/cnuw.ma".
+
+(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
+
+(* Properties with generic relocation ***************************************)
+
+lemma cnuw_lifts (h) (G): d_liftable1 … (cnuw h G).
+#h #G #K #T #HT #b #f #L #HLK #U #HTU #n #U0 #H
+elim (cpms_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
+lapply (HT … HT0) -G -K /2 width=6 by tweq_lifts_bi/
+qed-.
+
+(* Inversion lemmas with generic relocation *********************************)
+
+lemma cnuw_inv_lifts (h) (G): d_deliftable1 … (cnuw h G).
+#h #G #L #U #HU #b #f #K #HLK #T #HTU #n #T0 #H
+elim (cpms_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
+lapply (HU … HU0) -G -L /2 width=6 by tweq_inv_lifts_bi/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cnuw_lref (h) (I) (G) (L):
+      ∀i. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i → ⦃G,L.ⓘ{I}⦄ ⊢ ➡𝐍𝐖*[h] #↑i.
+#h #I #G #L #i #Hi #n #X2 #H
+elim (cpms_inv_lref_sn … H) -H *
+[ #H #_ destruct //
+| #T2 #HT2 #HTX2
+  lapply (Hi … HT2) -Hi -HT2 #H
+  lapply (tweq_inv_lref_sn … H) -H #H destruct
+  lapply (lifts_inv_lref1_uni … HTX2) -HTX2 #H destruct //
+]
+qed.
+
+lemma cnuw_atom_drops (h) (b) (G) (L):
+      ∀i. ⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i.
+#h #b #G #L #i #Hi #n #X #H
+elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #K #V1 #V2 #HLK
+lapply (drops_gen b … HLK) -HLK #HLK
+lapply (drops_mono … Hi … HLK) -L #H destruct
+qed.
+
+lemma cnuw_unit_drops (h) (I) (G) (L):
+      ∀K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i.
+#h #I #G #L #K #i #HLK #n #X #H
+elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #Y #V1 #V2 #HLY
+lapply (drops_mono … HLK … HLY) -L #H destruct
+qed.