Merge branch 'matita-lablgtk3' of ssh://matita.cs.unibo.it:/srv/git/helm into matita...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cnr_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_drops.ma
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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 "basic_2/rt_transition/cpr_drops.ma".
+include "basic_2/rt_transition/cnr.ma".
+
+(* NORMAL TERMS FOR CONTEXT-SENSITIVE R-TRANSITION **************************)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_1: was only: nf2_csort_lref *)
+lemma cnr_lref_atom (h) (b) (G) (L):
+      ∀i. ⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄.
+#h #b #G #L #i #Hi #X #H
+elim (cpr_inv_lref1_drops … H) -H // * #K #V1 #V2 #HLK
+lapply (drops_gen b … HLK) -HLK #HLK
+lapply (drops_mono … Hi … HLK) -L #H destruct
+qed.
+
+(* Basic_1: was: nf2_lref_abst *)
+lemma cnr_lref_abst (h) (G) (L):
+      ∀K,V,i. ⬇*[i] L ≘ K.ⓛV → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄.
+#h #G #L #K #V #i #HLK #X #H
+elim (cpr_inv_lref1_drops … H) -H // *
+#K0 #V1 #V2 #HLK0 #_ #_
+lapply (drops_mono … HLK … HLK0) -L #H destruct
+qed.
+
+lemma cnr_lref_unit (h) (I) (G) (L):
+      ∀K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄.
+#h #I #G #L #K #i #HLK #X #H
+elim (cpr_inv_lref1_drops … H) -H // *
+#K0 #V1 #V2 #HLK0 #_ #_
+lapply (drops_mono … HLK … HLK0) -L #H destruct
+qed.
+
+(* Properties with generic relocation ***************************************)
+
+(* Basic_1: was: nf2_lift *)
+(* Basic_2A1: uses: cnr_lift *)
+lemma cnr_lifts (h) (G): d_liftable1 … (cnr h G).
+#h #G #K #T #HT #b #f #L #HLK #U #HTU #U0 #H
+elim (cpm_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
+lapply (HT … HT0) -G -K #H destruct /2 width=4 by lifts_mono/
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: was: cnr_inv_delta *)
+lemma cnr_inv_lref_abbr (h) (G) (L):
+      ∀K,V,i. ⬇*[i] L ≘ K.ⓓV → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄ → ⊥.
+#h #G #L #K #V #i #HLK #H
+elim (lifts_total V 𝐔❴↑i❵) #W #HVW
+lapply (H W ?) -H [ /3 width=6 by cpm_delta_drops/ ] -HLK #H destruct
+elim (lifts_inv_lref2_uni_lt … HVW) -HVW //
+qed-.
+
+(* Inversion lemmas with generic relocation *********************************)
+
+(* Note: this was missing in Basic_1 *)
+(* Basic_2A1: uses: cnr_inv_lift *)
+lemma cnr_inv_lifts (h) (G): d_deliftable1 … (cnr h G).
+#h #G #L #U #HU #b #f #K #HLK #T #HTU #T0 #H
+elim (cpm_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
+lapply (HU … HU0) -G -L #H destruct /2 width=4 by lifts_inj/
+qed-.