+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/static/frees_drops.ma".
-include "basic_2/static/fsle_length.ma".
-
-(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
-
-(* Advanced properties ******************************************************)
-
-lemma fsle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| →
- ∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄.
-#T1 #U1 #HTU1 #L1 #L2 #H1L #T2
-* #n #m #f #g #Hf #Hg #H2L #Hfg
-lapply (lveq_length_fwd_dx … H2L ?) // -H1L #H destruct
-lapply (frees_lifts_SO (Ⓣ) (L1.ⓧ) … HTU1 … Hf)
-[ /3 width=4 by drops_refl, drops_drop/ ] -T1 #Hf
-@(ex4_4_intro … Hf Hg) /2 width=4 by lveq_void_sn/ (**) (* explict constructor *)
-qed-.
-
-lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
- ∀W1. ⬆*[1] V1 ≘ W1 → ∀I1,I2. ⦃K1.ⓘ{I1}, W1⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
-#K1 #K2 #HK #V1 #V2
-* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
-#W1 #HVW1 #I1 #I2
-elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, sle_weak, ex4_4_intro/
-qed.
-
-lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ⦃K1, T1⦄ ⊆ ⦃K2, T2⦄ →
- ∀U1,U2. ⬆*[1] T1 ≘ U1 → ⬆*[1] T2 ≘ U2 →
- ∀I1,I2. ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄.
-#K1 #K2 #HK #T1 #T2
-* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
-#U1 #U2 #HTU1 #HTU2 #I1 #I2
-elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/
-qed.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma fsle_inv_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 →
- ∀I1,I2,L1,L2,V1,V2,U2. ⦃L1.ⓑ{I1}V1,U1⦄ ⊆ ⦃L2.ⓑ{I2}V2, U2⦄ →
- ∀p. ⦃L1, T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.U2⦄.
-#T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2
-* #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
-elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
-elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
-[1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2
-lapply (sor_inv_sle_dx … Hg) #H0g
-/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/
-qed-.