(* *)
(**************************************************************************)
-include "basic_2/rt_transition/fpb_ffdeq.ma".
+include "basic_2/rt_transition/fpb_fdeq.ma".
include "basic_2/rt_transition/fpbq.ma".
(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
(* Basic_2A1: fpb_fpbq_alt *)
lemma fpb_fpbq_ffdneq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
∧∧ ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ & (⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥).
-/3 width=10 by fpb_fpbq, fpb_inv_ffdeq, conj/ qed-.
+/3 width=10 by fpb_fpbq, fpb_inv_fdeq, conj/ qed-.
(* Inversrion lemmas with proper parallel rst-transition for closures *******)
| ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄.
#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
[ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
- /3 width=1 by fpb_fqu, ffdeq_intro_sn, or_intror, or_introl/
+ /3 width=1 by fpb_fqu, fdeq_intro_sn, or_intror, or_introl/
| #T2 #H elim (tdeq_dec h o T1 T2)
- /4 width=1 by fpb_cpx, ffdeq_intro_sn, or_intror, or_introl/
-| #L2 elim (lfdeq_dec h o L1 L2 T1)
- /4 width=1 by fpb_lpx, ffdeq_intro_sn, or_intror, or_introl/
+ /4 width=1 by fpb_cpx, fdeq_intro_sn, or_intror, or_introl/
+| #L2 elim (rdeq_dec h o L1 L2 T1)
+ /4 width=1 by fpb_lpx, fdeq_intro_sn, or_intror, or_introl/
| /2 width=1 by or_introl/
]
qed-.