1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/static/rdeq.ma".
16 include "static_2/static/aaa.ma".
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
20 (* Properties with degree-based equivalence on referred entries *************)
22 lemma aaa_tdeq_conf_rdeq: ∀h,o,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀T2. T1 ≛[h, o] T2 →
23 ∀L2. L1 ≛[h, o, T1] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
24 #h #o #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
25 [ #G #L1 #s1 #X #H1 elim (tdeq_inv_sort1 … H1) -H1 //
26 | #I #G #L1 #V1 #B #_ #IH #X #H1 >(tdeq_inv_lref1 … H1) -H1
27 #Y #H2 elim (rdeq_inv_zero_pair_sn … H2) -H2
28 #L2 #V2 #HL12 #HV12 #H destruct /3 width=1 by aaa_zero/
29 | #I #G #L1 #A #i #_ #IH #X #H1 >(tdeq_inv_lref1 … H1) -H1
30 #Y #H2 elim (rdeq_inv_lref_bind_sn … H2) -H2
31 #J #L2 #HL12 #H destruct /3 width=1 by aaa_lref/
32 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
33 #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_bind … H2) -H2 destruct
34 /5 width=2 by aaa_abbr, rdeq_bind_repl_dx, ext2_pair/
35 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
36 #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_bind … H2) -H2 destruct
37 /5 width=2 by aaa_abst, rdeq_bind_repl_dx, ext2_pair/
38 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
39 #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_flat … H2) -H2 destruct
40 /3 width=3 by aaa_appl/
41 | #G #L1 #V1 #T1 #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
42 #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_flat … H2) -H2 destruct
43 /3 width=1 by aaa_cast/