update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / llor.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/llor.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/llor.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_2A/notation/relations/lazyor_5.ma".
+include "basic_2A/multiple/frees.ma".
+
+(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
+
+definition llor: ynat → relation4 term lenv lenv lenv ≝ λl,T,L2,L1,L.
+                 ∧∧ |L1| = |L2| & |L1| = |L|
+                  & (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
+                       ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 → ⬇[i] L ≡ K.ⓑ{I}V → ∨∨
+                       (∧∧ yinj i < l & I1 = I & V1 = V) |
+                       (∧∧ (L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ → ⊥) & I1 = I & V1 = V) |
+                       (∧∧ l ≤ yinj i & L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ & I2 = I & V2 = V)
+                    ).
+
+interpretation
+   "lazy union (local environment)"
+   'LazyOr L1 T l L2 L = (llor l T L2 L1 L).
+
+(* Basic properties *********************************************************)
+
+(* Note: this can be proved by llor_skip *)
+lemma llor_atom: ∀T,l. ⋆ ⋓[T, l] ⋆ ≡ ⋆.
+#T #l @and3_intro //
+#I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
+elim (drop_inv_atom1 … HLK1) -HLK1 #H destruct
+qed.