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 include "basic_2/computation/acp_aaa.ma".
 include "basic_2/computation/csn_tstc_vector.ma".
 
-(* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
 
-(* Properties concerning atomic arity assignment ****************************)
+(* Main properties concerning atomic arity assignment ***********************)
 
-lemma csn_aaa: ∀L,T,A. L ⊢ T ⁝ A → L ⊢ ⬊* T.
-#L #T #A #H
-@(acp_aaa … csn_acp csn_acr … H)
-qed. 
+theorem csn_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ⦃h, L⦄ ⊢ ⬊*[g] T.
+#h #g #L #T #A #H
+@(acp_aaa … (csn_acp h g) (csn_acr h g) … H)
+qed.