include "basic_2/reduction/cpr_cir.ma".
include "basic_2/reduction/cnr_crr.ma".
-(* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
+(* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
-(* Main properties on context-sensitive irreducible terms *******************)
+(* Main properties on irreducibility ****************************************)
-theorem cir_cnr: ∀L,T. ⦃G, L⦄ ⊢ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍⦃T⦄.
-/2 width=3 by cpr_fwd_cir/ qed.
+theorem cir_cnr: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
+/2 width=4 by cpr_fwd_cir/ qed.
-(* Main inversion lemmas on context-sensitive irreducible terms *************)
+(* Main inversion lemmas on irreducibility **********************************)
-theorem cnr_inv_cir: ∀L,T. ⦃G, L⦄ ⊢ 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃T⦄.
-/2 width=4 by cnr_inv_crr/ qed-.
+theorem cnr_inv_cir: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄.
+/2 width=5 by cnr_inv_crr/ qed-.