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3 (*      ||M||                                                             *)
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10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "basic_2/reduction/cpr_cir.ma".
16 include "basic_2/reduction/cnr_crr.ma".
17
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
19
20 (* Main properties on irreducibility ****************************************)
21
22 theorem cir_cnr: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
23 /2 width=4 by cpr_fwd_cir/ qed.
24
25 (* Main inversion lemmas on irreducibility **********************************)
26
27 theorem cnr_inv_cir: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄.
28 /2 width=5 by cnr_inv_crr/ qed-.