(* *)
(**************************************************************************)
+include "ground_2/xoa/ex_2_3.ma".
include "basic_2/notation/relations/predsubtystarproper_7.ma".
include "basic_2/rt_transition/fpb.ma".
include "basic_2/rt_computation/fpbs.ma".
qed-.
lemma fpbg_fqu_trans (h): ∀G1,G,G2,L1,L,L2,T1,T,T2.
- â¦\83G1,L1,T1â¦\84 >[h] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â\8a\90 ⦃G2,L2,T2⦄ →
+ â¦\83G1,L1,T1â¦\84 >[h] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82 ⦃G2,L2,T2⦄ →
⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
qed-.
(* Basic_2A1: uses: fpbg_fleq_trans *)
-lemma fpbg_fdeq_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G,L,T⦄ →
+lemma fpbg_feqx_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G,L,T⦄ →
∀G2,L2,T2. ⦃G,L,T⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
-/3 width=5 by fpbg_fpbq_trans, fpbq_fdeq/ qed-.
+/3 width=5 by fpbg_fpbq_trans, fpbq_feqx/ qed-.
(* Properties with t-bound rt-transition for terms **************************)
-lemma cpm_tdneq_cpm_fpbg (h) (G) (L):
+lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
∀n1,T1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → ⦃G,L,T1⦄ >[h] ⦃G,L,T2⦄.
-/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.
+/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.