- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpa / fpas_vector.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/fpas_vector.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/fpas_vector.etc
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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/grammar/term_vector.ma".
+include "basic_2/multiple/fpas.ma".
+
+(* MULTIPLE VECTOR AJUSTMENT ************************************************)
+
+inductive fpasv (s:bool): bi_relation lenv (list term) ≝
+| fpasv_nil : ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄  → fpasv s L1 (◊) L2 (◊)
+| fpasv_cons: ∀L1,L2,T1s,T2s,T1,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄  →
+              fpasv s L1 T1s L2 T2s →
+              fpasv s L1 (T1 @ T1s) L2 (T2 @ T2s)
+.
+
+interpretation
+   "multiple vector ajustment (restricted closure)"
+   'RAjustStar L1 T1s s L2 T2s = (fpasv s L1 T1s L2 T2s).
+
+(* Basic inversion lemmas ***************************************************)
+
+
+
+(* Basic_1: was just: lifts1_flat (left to right) *)
+lemma fpas_inv_applv1: ∀L1,L2,V1s,T1,X,s. ⦃L1, Ⓐ V1s.T1⦄ ⇳*[s] ⦃L2, X⦄ →
+                       ∃∃V2s,T2. ⦃L1, V1s⦄ ⇳*[s] ⦃L2, V2s⦄ & ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ &
+                                 X = Ⓐ V2s.T2.
+#L1 #L2 #V1s elim V1s -V1s
+[ #T1 #X #s #H
+  @(ex3_2_intro … (◊) X) /2 width=3 by fpasv_nil/ (**) (* explicit constructor *)
+| #V1 #V1s #IHV1s #T1 #X #s #H
+  elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
+  elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
+  @(ex3_2_intro) [4: // |3: /2 width=2 by liftsv_cons/ |1,2: skip | // ] (**) (* explicit constructor *)
+]
+qed-.
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was just: lifts1_flat (right to left) *)
+lemma lifts_applv: ∀V1s,V2s,des. ⇧*[des] V1s ≡ V2s →
+                   ∀T1,T2. ⇧*[des] T1 ≡ T2 →
+                   ⇧*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
+#V1s #V2s #des #H elim H -V1s -V2s /3 width=1 by lifts_flat/
+qed.