(* Advanced properties with sort-irrelevant equivalence for terms ***********)
-lemma fpbg_teqx_div: â\88\80h,G1,G2,L1,L2,T1,T. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,Tâ¦\84 →
- â\88\80T2. T2 â\89\9b T â\86\92 â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84.
+lemma fpbg_teqx_div: â\88\80h,G1,G2,L1,L2,T1,T. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,Tâ\9d« →
+ â\88\80T2. T2 â\89\9b T â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
/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¬\82+ â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84.
+lemma fqup_fpbg: â\88\80h,G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82+ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
#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.