still more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_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 "static_2/relocation/drops.ma".
+include "basic_2/rt_computation/jsx.ma".
+
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+
+(* Forward lemmas with uniform slicing for local environments ***************)
+
+lemma jsx_fwd_drops_atom_sn (h) (b) (G):
+      ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
+      ∀f. 𝐔⦃f⦄ → ⬇*[b,f]L1 ≘ ⋆ → ⬇*[b,f]L2 ≘ ⋆.
+#h #b #G #L1 #L2 #H elim H -L1 -L2
+[ #f #_ #H //
+| #I #K1 #K2 #_ #IH #f #Hf #H
+| #I #K1 #K2 #V #_ #HV #IH #f #Hf #H
+]
+elim (drops_inv_bind1_isuni … H) -H [3,6: // |*: * -Hf ]
+[1,3: #_ #H destruct
+|2,4: #g #Hg #HK1 #H destruct /3 width=1 by drops_drop/
+]
+qed-.
+
+lemma jsx_fwd_drops_unit_sn (h) (b) (G):
+      ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
+      ∀f. 𝐔⦃f⦄ → ∀I,K1. ⬇*[b,f]L1 ≘ K1.ⓤ{I} →
+      ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓤ{I}.
+#h #b #G #L1 #L2 #H elim H -L1 -L2
+[ #f #_ #J #Y1 #H
+  lapply (drops_inv_atom1 … H) -H * #H #_ destruct
+| #I #K1 #K2 #HK12 #IH #f #Hf #J #Y1 #H
+| #I #K1 #K2 #V #HK12 #HV #IH #f #Hf #J #Y1 #H
+]
+elim (drops_inv_bind1_isuni … H) -H [3,6: // |*: * -Hf ]
+[1,3: #Hf #H destruct -IH /3 width=3 by drops_refl, ex2_intro/
+|2,4:
+  #g #Hg #HK1 #H destruct
+  elim (IH … Hg … HK1) -K1 -Hg #Y2 #HY12 #HKY2 
+  /3 width=3 by drops_drop, ex2_intro/
+]
+qed-.
+
+lemma jsx_fwd_drops_pair_sn (h) (b) (G):
+      ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
+      ∀f. 𝐔⦃f⦄ → ∀I,K1,V. ⬇*[b,f]L1 ≘ K1.ⓑ{I}V →
+      ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓑ{I}V
+       | ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓧ & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄.
+#h #b #G #L1 #L2 #H elim H -L1 -L2
+[ #f #_ #J #Y1 #X1 #H
+  lapply (drops_inv_atom1 … H) -H * #H #_ destruct
+| #I #K1 #K2 #HK12 #IH #f #Hf #J #Y1 #X1 #H
+| #I #K1 #K2 #V #HK12 #HV #IH #f #Hf #J #Y1 #X1 #H
+]
+elim (drops_inv_bind1_isuni … H) -H [3,6: // |*: * -Hf ]
+[1,3:
+  #Hf #H destruct -IH
+  /4 width=4 by drops_refl, ex3_intro, ex2_intro, or_introl, or_intror/
+|2,4:
+  #g #Hg #HK1 #H destruct
+  elim (IH … Hg … HK1) -K1 -Hg * #Y2 #HY12 #HKY2 [2,4: #HX1 ]
+  /4 width=4 by drops_drop, ex3_intro, ex2_intro, or_introl, or_intror/
+]
+qed-.