(* *)
(**************************************************************************)
-include "basic_2/static/ffdeq_fqup.ma".
-include "basic_2/static/ffdeq_ffdeq.ma".
+include "basic_2/static/fdeq_fqup.ma".
+include "basic_2/static/fdeq_fdeq.ma".
include "basic_2/rt_transition/fpbq_fpb.ma".
include "basic_2/rt_computation/fpbg.ma".
(* Advanced properties with degree-based equivalence on closures ************)
(* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma ffdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
- ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
+lemma fdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
+ ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
#h #o #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
-elim (ffdeq_fpb_trans … H1 … H0) -G -L -T
-/4 width=9 by fpbs_strap2, fpbq_ffdeq, ex2_3_intro/
+elim (fdeq_fpb_trans … H1 … H0) -G -L -T
+/4 width=9 by fpbs_strap2, fpbq_fdeq, ex2_3_intro/
qed-.
(* Properties with parallel proper rst-reduction on closures ****************)
⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
elim (fpbq_inv_fpb … H1) -H1
-/2 width=5 by ffdeq_fpbg_trans, fpb_fpbg_trans/
+/2 width=5 by fdeq_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 ffdeq_trans, or_introl/
- | elim (ffdeq_fpb_trans … H1 … H2) -G -L -T
- /4 width=5 by ex2_3_intro, or_intror, ffdeq_fpbs/
- | /3 width=5 by fpbg_ffdeq_trans, or_intror/
+ [ /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/
| /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
]
]
∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
#h #o #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
-[ #H12 #G2 #L2 #U2 #H2 elim (ffdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
- /3 width=5 by ffdeq_fpbs, ex2_3_intro/
+[ #H12 #G2 #L2 #U2 #H2 elim (fdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
+ /3 width=5 by fdeq_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/
]