include "basic_2/multiple/frees_leq.ma".
include "basic_2/multiple/frees_lift.ma".
-include "basic_2/reduction/lpx_ldrop.ma".
+include "basic_2/reduction/lpx_drop.ma".
(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
| #j #HG #HL #HU #U2 #H1 #L2 #HL12 #i #H2 elim (cpx_inv_lref1 … H1) -H1
[ #H destruct elim (frees_inv_lref … H2) -H2 //
* #I #K2 #W2 #Hj #Hji #HLK2 #HW2
- elim (lpx_ldrop_trans_O1 … HL12 … HLK2) -HL12 #Y #HLK1 #H
+ elim (lpx_drop_trans_O1 … HL12 … HLK2) -HL12 #Y #HLK1 #H
elim (lpx_inv_pair2 … H) -H #K1 #W1 #HK12 #HW12 #H destruct
/4 width=11 by frees_lref_be, fqup_lref/
| * #I #K1 #W1 #W0 #HLK1 #HW10 #HW0U2
- lapply (ldrop_fwd_drop2 … HLK1) #H0
- elim (lpx_ldrop_conf … H0 … HL12) -H0 -HL12 #K2 #HK12 #HLK2
+ lapply (drop_fwd_drop2 … HLK1) #H0
+ elim (lpx_drop_conf … H0 … HL12) -H0 -HL12 #K2 #HK12 #HLK2
elim (lt_or_ge i (j+1)) #Hji
[ -IH elim (frees_inv_lift_be … H2 … HLK2 … HW0U2) /2 width=1 by monotonic_pred/
| lapply (frees_inv_lift_ge … H2 … HLK2 … HW0U2 ?) -L2 -U2 // <minus_plus destruct
/4 width=7 by frees_bind_dx_O, frees_bind_sn, lpx_pair/
| #U2 #HU12 #HXU2 #H1 #H2 destruct
lapply (frees_lift_ge … Hi (L2.ⓓW1) (Ⓕ) … HXU2 ?)
- /4 width=7 by frees_bind_dx_O, lpx_pair, ldrop_drop/
+ /4 width=7 by frees_bind_dx_O, lpx_pair, drop_drop/
]
| #I #W1 #X1 #HG #HL #HU #X2 #HX2 #L2 #HL12 #i #Hi destruct
elim (cpx_inv_flat1 … HX2) -HX2 *
[ /4 width=7 by frees_flat_dx, frees_bind_sn/
| elim (frees_inv_flat … Hi) -Hi
[ #HW0 lapply (frees_inv_lift_ge … HW0 L2 (Ⓕ) … HW20 ?) -W0
- /3 width=7 by frees_flat_sn, ldrop_drop/
+ /3 width=7 by frees_flat_sn, drop_drop/
| /5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/
]
]