(* Properties with atomic atomic arity assignment on terms ******************)
lemma cpmre_total_aaa (h) (n) (A) (G) (L):
- ∀T1. ❪G,L❫ ⊢ T1 ⁝ A → ∃T2. ❪G,L❫ ⊢ T1 ➡*[h,n] 𝐍❪T2❫.
+ ∀T1. ❪G,L❫ ⊢ T1 ⁝ A → ∃T2. ❪G,L❫ ⊢ T1 ➡*𝐍[h,n] T2.
#h #n #A #G #L #T1 #HT1
elim (cpms_total_aaa h … n … HT1) #T0 #HT10
elim (cprre_total_csx h G L T0)
[ #T2 /3 width=4 by cpms_cprre_trans, ex_intro/
-| /4 width=4 by cpms_fwd_cpxs, aaa_csx, csx_cpxs_trans/
+| /4 width=5 by cpms_fwd_cpxs, aaa_csx, csx_cpxs_trans/
]
qed-.