(* Advanced properties with sort-irrelevant equivalence for terms ***********)
-lemma fpbg_tdeq_div: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T⦄ →
+lemma fpbg_teqx_div: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T⦄ →
∀T2. T2 ≛ T → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
-/4 width=5 by fpbg_fdeq_trans, tdeq_fdeq, tdeq_sym/ qed-.
+/4 width=5 by fpbg_feqx_trans, teqx_feqx, teqx_sym/ qed-.
(* Properties with plus-iterated structural successor for closures **********)
(* Note: this is used in the closure proof *)
-lemma fqup_fpbg: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90+ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+lemma fqup_fpbg: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqup_inv_step_sn … H) -H
/3 width=5 by fqus_fpbs, fpb_fqu, ex2_3_intro/
qed.