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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                  *)
(*                                                                        *)
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include "basic_2/computation/scpds_aaa.ma".
include "basic_2/equivalence/scpes.ma".

(* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)

(* Main inversion lemmas about atomic arity assignment on terms *************)

theorem scpes_aaa_mono: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
                        ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
                        A1 = A2.
#h #o #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #A1 #HA1 #A2 #HA2
lapply (scpds_aaa_conf … HA1 … HT1) -T1 #HA1
lapply (scpds_aaa_conf … HA2 … HT2) -T2 #HA2
lapply (aaa_mono … HA1 … HA2) -L -T //
qed-.