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 / cpx_drops_basic.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops_basic.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops_basic.ma
new file mode 100644 (file)
index 0000000..12d23e2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops_basic.ma
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_basic.ma".
+include "basic_2/rt_transition/cpx_drops.ma".
+
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+
+(* Properties with basic relocation *****************************************)
+
+lemma cpx_subst (h) (G) (L) (U1) (i):
+                ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V →
+                ∃∃U2,T2. ⦃G,L⦄ ⊢ U1 ⬈[h] U2 & ⬆[i,1] T2 ≘ U2.
+#h #G #L #U1 @(fqup_wf_ind_eq (Ⓣ) … G L U1) -G -L -U1
+#G0 #L0 #U0 #IH #G #L * *
+[ #s #HG #HL #HT #i #I #K #V #_ destruct -IH
+  /2 width=4 by lifts_sort, ex2_2_intro/
+| #j #HG #HL #HT #i #I #K #V #HLK destruct -IH
+  elim (lt_or_eq_or_gt i j) #Hij
+  [ /3 width=4 by lifts_lref_ge_minus, cpx_refl, ex2_2_intro/
+  | elim (lifts_total V (𝐔❴↑i❵)) #U2 #HU2
+    elim (lifts_split_trans … HU2 (𝐔❴i❵) (𝐁❴i,1❵)) [2: @(after_basic_rc i 0) ]
+    /3 width=7 by cpx_delta_drops, ex2_2_intro/
+  | /3 width=4 by lifts_lref_lt, cpx_refl, ex2_2_intro/
+  ]
+| #l #HG #HL #HT #i #I #K #V #_ destruct -IH
+  /2 width=4 by lifts_gref, ex2_2_intro/
+| #p #J #W1 #U1 #HG #HL #HT #i #I #K #V #HLK destruct
+  elim (IH G L W1 … HLK) [| // ] #W2 #V2 #HW12 #HVW2
+  elim (IH G (L.ⓑ{J}W1) U1 … (↑i)) [|*: /3 width=4 by drops_drop/ ] #U2 #T2 #HU12 #HTU2
+  /3 width=9 by cpx_bind, lifts_bind, ex2_2_intro/
+| #J #W1 #U1 #HG #HL #HT #i #I #K #V #HLK destruct
+  elim (IH G L W1 … HLK) [| // ] #W2 #V2 #HW12 #HVW2
+  elim (IH G L U1 … HLK) [| // ] #U2 #T2 #HU12 #HTU2
+  /3 width=8 by cpx_flat, lifts_flat, ex2_2_intro/
+]
+qed-.