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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/reduction/crx.ma".
16 include "basic_2/reduction/cnx.ma".
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
20 (* Advanced inversion lemmas on reducibility ********************************)
22 (* Note: this property is unusual *)
23 lemma cnx_inv_crx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ → ⊥.
24 #h #o #G #L #T #H elim H -L -T
26 lapply (cnx_inv_sort … H) -H #H
27 lapply (deg_mono … H Hkd) -h -L -s <plus_n_Sm #H destruct
28 | #I #L #K #V #i #HLK #H
29 elim (cnx_inv_delta … HLK H)
31 elim (cnx_inv_appl … H) -H /2 width=1 by/
33 elim (cnx_inv_appl … H) -H /2 width=1 by/
34 | #I #L #V #T * #H1 #H2 destruct
35 [ elim (cnx_inv_zeta … H2)
36 | elim (cnx_inv_eps … H2)
38 |6,7: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
39 [1,3: elim (cnx_inv_abbr … H2) -H2 /2 width=1 by/
40 |*: elim (cnx_inv_abst … H2) -H2 /2 width=1 by/
43 elim (cnx_inv_appl … H) -H #_ #_ #H
44 elim (simple_inv_bind … H)
46 elim (cnx_inv_appl … H) -H #_ #_ #H
47 elim (simple_inv_bind … H)