(* *)
(**************************************************************************)
-include "static_2/static/fdeq_fdeq.ma".
+include "static_2/static/feqx_feqx.ma".
include "basic_2/rt_transition/fpbq_fpb.ma".
include "basic_2/rt_computation/fpbs_fqup.ma".
include "basic_2/rt_computation/fpbg.ma".
(* Advanced properties with sort-irrelevant equivalence on closures *********)
(* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma fdeq_fpbg_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ →
+lemma feqx_fpbg_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ →
∀G1,L1,T1. ⦃G1,L1,T1⦄ ≛ ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
#h #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
-elim (fdeq_fpb_trans … H1 … H0) -G -L -T
-/4 width=9 by fpbs_strap2, fpbq_fdeq, ex2_3_intro/
+elim (feqx_fpb_trans … H1 … H0) -G -L -T
+/4 width=9 by fpbs_strap2, fpbq_feqx, ex2_3_intro/
qed-.
(* Properties with parallel proper rst-reduction on closures ****************)
⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
elim (fpbq_inv_fpb … H1) -H1
-/2 width=5 by fdeq_fpbg_trans, fpb_fpbg_trans/
+/2 width=5 by feqx_fpbg_trans, fpb_fpbg_trans/
qed-.
(* Properties with parallel rst-compuutation on closures ********************)
[ /2 width=1 by or_introl/
| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1
elim (fpbq_inv_fpb … H2) -H2 #H2
- [ /3 width=5 by fdeq_trans, or_introl/
- | elim (fdeq_fpb_trans … H1 … H2) -G -L -T
- /4 width=5 by ex2_3_intro, or_intror, fdeq_fpbs/
- | /3 width=5 by fpbg_fdeq_trans, or_intror/
+ [ /3 width=5 by feqx_trans, or_introl/
+ | elim (feqx_fpb_trans … H1 … H2) -G -L -T
+ /4 width=5 by ex2_3_intro, or_intror, feqx_fpbs/
+ | /3 width=5 by fpbg_feqx_trans, or_intror/
| /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
]
]
∀G2,L2,U2. ⦃F2,K2,T2⦄ ≻[h] ⦃G2,L2,U2⦄ →
∃∃G1,L1,U1. ⦃F1,K1,T1⦄ ≻[h] ⦃G1,L1,U1⦄ & ⦃G1,L1,U1⦄ ≥[h] ⦃G2,L2,U2⦄.
#h #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
-[ #H12 #G2 #L2 #U2 #H2 elim (fdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
- /3 width=5 by fdeq_fpbs, ex2_3_intro/
+[ #H12 #G2 #L2 #U2 #H2 elim (feqx_fpb_trans … H12 … H2) -F2 -K2 -T2
+ /3 width=5 by feqx_fpbs, ex2_3_intro/
| * #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9
@(ex2_3_intro … H4) -H4 /3 width=5 by fpbs_strap1, fpb_fpbq/
]