+(**************************************************************************)
+(* ___ *)
+(* ||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/fle_drops.ma".
+include "basic_2/static/fle_fqup.ma".
+include "basic_2/static/fle_fle.ma".
+include "basic_2/static/lfxs.ma".
+include "basic_2/rt_transition/cpx.ma".
+
+axiom fle_pair_sn: ∀L,V1,V2. ⦃L, V1⦄ ⊆ ⦃L, V2⦄ →
+ ∀I1,I2,T. ⦃L.ⓑ{I1}V1, T⦄ ⊆ ⦃L.ⓑ{I2}V2, T⦄.
+(*
+axiom fle_elim_flat: ∀L1,L2,V1,T2. ⦃L1, V1⦄ ⊆ ⦃L2, T2⦄ → ∀T1. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
+ ∀I. ⦃L1, ⓕ{I}V1.T1⦄ ⊆ ⦃L2, T2⦄.
+
+axiom fle_elim_bind:
+ ∀p,I1,I2,J1,J2,L,V,W,T. ⦃L, ⓑ{p,I1}ⓕ{J1}V.W.T⦄ ⊆ ⦃L, ⓕ{J2}V.ⓑ{p,I2}W.T⦄.
+*)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
+
+(* Properties with context-sensitive free variables *************************)
+
+(* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *)
+axiom cpx_lfxs_conf_gen: ∀R. c_reflexive … R →
+ ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
+ ∀L2. L0 ⪤*[R, T0] L2 →
+ ∧∧ ⦃L2, T0⦄ ⊆ ⦃L0, T0⦄ & ⦃L2, T1⦄ ⊆ ⦃L2, T0⦄
+ & ⦃L0, T1⦄ ⊆ ⦃L0, T0⦄.
+(*
+#R #HR #h #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -L0 -T0
+#G #L #T #IH #G0 #L0 * *
+[ #s #HG #HL #HT #X #HX #Y #_ destruct -IH
+ elim (cpx_inv_sort1 … HX) -HX #H destruct
+ /2 width=1 by and3_intro/
+|
+| #l #HG #HL #HT #X #HX #Y #_ destruct -IH
+ >(cpx_inv_gref1 … HX) -X
+ /2 width=1 by and3_intro/
+| #p #I #V0 #T0 #HG #HL #HT #X #HX #Y #HY destruct
+ elim (lfxs_inv_bind … V0 ? HY) -HY // #HV0 #HT0
+ elim (cpx_inv_bind1 … HX) -HX *
+ [ #V1 #T1 #HV01 #HT01 #H destruct
+ elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+ elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T
+ /5 width=4 by fle_pair_sn, fle_trans, fle_bind, and3_intro/
+ | #T #HT #HXT #H1 #H2 destruct
+ elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V
+ elim (IH … HT … HT0) -HT -HT0 -IH // #H1T #H2T #H3T
+ /4 width=7 by fle_bind_dx, fle_trans, fle_bind, and3_intro/
+ ]
+| #I #V0 #X0 #HG #HL #HT #X #HX #Y #HY destruct
+ elim (lfxs_inv_flat … HY) -HY #HV0 #HX0
+ elim (cpx_inv_flat1 … HX) -HX *
+ [ #V1 #T1 #HV01 #HT01 #H destruct
+ elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+ elim (IH … HT01 … HX0) -HT01 -HX0 -IH // #H1T #H2T #H3T
+ /3 width=3 by fle_flat, and3_intro/
+ | #HX #H destruct
+ elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V
+ elim (IH … HX … HX0) -HX -HX0 -IH // #H1T #H2T #H3T
+ /4 width=4 by fle_trans, fle_flat, and3_intro/
+ | #HX #H destruct
+ elim (IH … HX … HV0) -HX -HV0 // #H1V #H2V #H3V
+ elim (IH G0 … X0… X0 … HX0) -HX0 -IH // #H1T #H2T #H3T
+ /4 width=4 by fle_trans, fle_flat, and3_intro/
+ | #p #V1 #W0 #W1 #T0 #T1 #HV01 #HW01 #HT01 #H1 #H2 #H3 destruct
+ elim (lfxs_inv_bind … W0 ? HX0) -HX0 // #HW0 #HT0
+ elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+ elim (IH … HW01 … HW0) -HW01 -HW0 // #H1W #H2W #H3W
+ elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T
+ @and3_intro
+ [ /3 width=5 by fle_flat, fle_bind/
+ | @(fle_trans)
+ [4: @(fle_flat … H2V) [2: @(fle_bind … H2T) // | skip | @Appl ]
+ |1,2: skip
+ | @(fle_trans) [3: @fle_elim_bind
+
+ … H2T) //
+
+ // |1,2: skip
+ | /2 width=1 by fle_bind_dx/
+*)