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14
15 include "basic_2/reduction/crr.ma".
16 include "basic_2/reduction/cnr.ma".
17
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
19
20 (* Advanced inversion lemmas on reducibility ********************************)
21
22 (* Note: this property is unusual *)
23 lemma cnr_inv_crr: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → ⊥.
24 #G #L #T #H elim H -L -T
25 [ #L #K #V #i #HLK #H
26   elim (cnr_inv_delta … HLK H)
27 | #L #V #T #_ #IHV #H
28   elim (cnr_inv_appl … H) -H /2 width=1 by/
29 | #L #V #T #_ #IHT #H
30   elim (cnr_inv_appl … H) -H /2 width=1 by/
31 | #I #L #V #T * #H1 #H2 destruct
32   [ elim (cnr_inv_zeta … H2)
33   | elim (cnr_inv_eps … H2)
34   ]
35 |5,6: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
36   [1,3: elim (cnr_inv_abbr … H2) -H2 /2 width=1 by/
37   |*: elim (cnr_inv_abst … H2) -H2 /2 width=1 by/
38   ]
39 | #a #L #V #W #T #H
40   elim (cnr_inv_appl … H) -H #_ #_ #H
41   elim (simple_inv_bind … H)
42 | #a #L #V #W #T #H
43   elim (cnr_inv_appl … H) -H #_ #_ #H
44   elim (simple_inv_bind … H)
45 ]
46 qed-.