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refactoring to park the notions:
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_new / cnx / cnx_crx.etc
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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/crx.ma".
16 include "basic_2/reduction/cnx.ma".
17
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
19
20 (* Advanced inversion lemmas on reducibility ********************************)
21
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
25 [ #L #s #d #Hkd #H
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)
30 | #L #V #T #_ #IHV #H
31   elim (cnx_inv_appl … H) -H /2 width=1 by/
32 | #L #V #T #_ #IHT #H
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)
37   ]
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/
41   ]
42 | #a #L #V #W #T #H
43   elim (cnx_inv_appl … H) -H #_ #_ #H
44   elim (simple_inv_bind … H)
45 | #a #L #V #W #T #H
46   elim (cnx_inv_appl … H) -H #_ #_ #H
47   elim (simple_inv_bind … H)
48 ]
49 qed-.