(* Properties with sort-irrelevant equivalence for local environments *******)
lemma cpms_reqx_conf_sn (h) (n) (G) (L1) (L2):
- ∀T1,T2. ❪G,L1❫ ⊢ T1 ➡*[n,h] T2 →
+ ∀T1,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 →
L1 ≛[T1] L2 → L1 ≛[T2] L2.
/3 width=5 by cpms_fwd_cpxs, cpxs_reqx_conf_sn/ qed-.
lemma cpms_reqx_conf_dx (h) (n) (G) (L1) (L2):
- ∀T1,T2. ❪G,L2❫ ⊢ T1 ➡*[n,h] T2 →
+ ∀T1,T2. ❪G,L2❫ ⊢ T1 ➡*[h,n] T2 →
L1 ≛[T1] L2 → L1 ≛[T2] L2.
/3 width=5 by cpms_fwd_cpxs, cpxs_reqx_conf_dx/ qed-.