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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/static/lsubr_length.ma".
include "basic_2/rt_transition/lfpx_fsle.ma".

lemma pippo: ∀L1,L2. L2 ⫃ L1 → ∀T. ⦃L1, T⦄ ⊆ ⦃L2, T⦄. 
#L1 #L2 #HL #T
elim (frees_total L1 T) #f1 #Hf1
elim (frees_total L2 T) #f2 #Hf2
lapply (lsubr_lsubf … Hf1 … HL … Hf2) #H
lapply (lsubf_fwd_sle … H) -H #H12
lapply (lsubr_fwd_length … HL) -HL #HL
/3 width=8 by lveq_length_eq, ex4_4_intro/
qed.

lemma R_fle_comp_LTC: ∀R. R_fle_compatible R → R_fle_compatible (LTC … R).
#R #HR #L #T1 #T2 #H elim H -T2
/3 width=3 by fle_trans_dx/
qed-.