(* Properties with sort-irrelevant equivalence for local environments *******)
-(* Basic_2A1: was just: lleq_cpxs_trans *)
+(* Basic_2A1: was just: lleq_cpxs_trans *)
lemma reqx_cpxs_trans: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
∀L2. L2 ≛[T0] L0 →
∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
/3 width=5 by cpxs_strap2, teqx_trans, ex2_intro/
qed-.
-(* Basic_2A1: was just: cpxs_lleq_conf *)
+(* Basic_2A1: was just: cpxs_lleq_conf *)
lemma cpxs_reqx_conf: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
∀L2. L0 ≛[T0] L2 →
∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
/3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
-(* Basic_2A1: was just: cpxs_lleq_conf_dx *)
+(* Basic_2A1: was just: cpxs_lleq_conf_dx *)
lemma cpxs_reqx_conf_dx: ∀h,G,L2,T1,T2. ⦃G,L2⦄ ⊢ 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 *)
+(* Basic_2A1: was just: lleq_conf_sn *)
lemma cpxs_reqx_conf_sn: ∀h,G,L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬈*[h] T2 →
∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
/4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.