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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/grammar/lenv_length.ma".
include "basic_2/grammar/cl_restricted_weight.ma".
include "basic_2/relocation/frees.ma".

(* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)

(* Forward lemmas on length for local environments **************************)

lemma frees_fwd_length: ∀L,T,t. L ⊢ 𝐅*⦃T⦄ ≡ t → |L| = |t|.
#L #T #t #H elim H -L -T -t //
[ #p ] #I #L #V #T #t1 #t2 #t [ #b ] #_ #_ #Ht elim (sor_inv_length … Ht) -Ht //
qed-.