(* Properties with sort-irrelevant equivalence for local environments *******)
(* Basic_2A1: was just: lleq_cpxs_trans *)
-lemma reqx_cpxs_trans: â\88\80h,G,L0,T0,T1. â¦\83G,L0â¦\84 ⊢ T0 ⬈*[h] T1 →
+lemma reqx_cpxs_trans: â\88\80h,G,L0,T0,T1. â\9dªG,L0â\9d« ⊢ T0 ⬈*[h] T1 →
∀L2. L2 ≛[T0] L0 →
- â\88\83â\88\83T. â¦\83G,L2â¦\84 ⊢ T0 ⬈*[h] T & T ≛ T1.
+ â\88\83â\88\83T. â\9dªG,L2â\9d« ⊢ T0 ⬈*[h] T & T ≛ T1.
#h #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
#T0 #T #HT0 #_ #IH #L2 #HL2
elim (reqx_cpx_trans … HL2 … HT0) #U1 #H1 #H2
qed-.
(* Basic_2A1: was just: cpxs_lleq_conf *)
-lemma cpxs_reqx_conf: â\88\80h,G,L0,T0,T1. â¦\83G,L0â¦\84 ⊢ T0 ⬈*[h] T1 →
+lemma cpxs_reqx_conf: â\88\80h,G,L0,T0,T1. â\9dªG,L0â\9d« ⊢ T0 ⬈*[h] T1 →
∀L2. L0 ≛[T0] L2 →
- â\88\83â\88\83T. â¦\83G,L2â¦\84 ⊢ T0 ⬈*[h] T & T ≛ T1.
+ â\88\83â\88\83T. â\9dªG,L2â\9d« ⊢ T0 ⬈*[h] T & T ≛ T1.
/3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
(* Basic_2A1: was just: cpxs_lleq_conf_dx *)
-lemma cpxs_reqx_conf_dx: â\88\80h,G,L2,T1,T2. â¦\83G,L2â¦\84 ⊢ T1 ⬈*[h] T2 →
+lemma cpxs_reqx_conf_dx: â\88\80h,G,L2,T1,T2. â\9dªG,L2â\9d« ⊢ T1 ⬈*[h] T2 →
∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
#h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
qed-.
(* Basic_2A1: was just: lleq_conf_sn *)
-lemma cpxs_reqx_conf_sn: â\88\80h,G,L1,T1,T2. â¦\83G,L1â¦\84 ⊢ T1 ⬈*[h] T2 →
+lemma cpxs_reqx_conf_sn: â\88\80h,G,L1,T1,T2. â\9dªG,L1â\9d« ⊢ T1 ⬈*[h] T2 →
∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
/4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.