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11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "static_2/static/reqg_fqup.ma".
16 include "static_2/static/aaa.ma".
17
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
19
20 (* Properties with generic equivalence on referred entries ******************)
21
22 lemma aaa_teqg_conf_reqg (S) (G):
23       reflexive … S →
24       ∀L1,T1,A. ❨G,L1❩ ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 →
25       ∀L2. L1 ≛[S,T1] L2 → ❨G,L2❩ ⊢ T2 ⁝ A.
26 #S #G #HS #L1 #T1 #A #H elim H -G -L1 -T1 -A
27 [ #G #L1 #s1 #X #H1 elim (teqg_inv_sort1 … H1) -H1 //
28 | #I #G #L1 #V1 #B #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
29   #Y #H2 elim (reqg_inv_zero_pair_sn … H2) -H2
30   #L2 #V2 #HL12 #HV12 #H destruct /3 width=1 by aaa_zero/
31 | #I #G #L1 #A #i #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
32   #Y #H2 elim (reqg_inv_lref_bind_sn … H2) -H2
33   #J #L2 #HL12 #H destruct /3 width=1 by aaa_lref/
34 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
35   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
36   /5 width=2 by aaa_abbr, reqg_bind_repl_dx, ext2_pair/
37 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
38   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
39   /5 width=2 by aaa_abst, reqg_bind_repl_dx, ext2_pair/
40 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
41   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
42   /3 width=3 by aaa_appl/
43 | #G #L1 #V1 #T1 #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
44   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
45   /3 width=1 by aaa_cast/
46 ]
47 qed-.
48
49 lemma aaa_teqg_conf (S) (G) (L) (A):
50       reflexive … S →
51       ∀T1. ❨G,L❩ ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 → ❨G,L❩ ⊢ T2 ⁝ A.
52 /3 width=7 by aaa_teqg_conf_reqg, reqg_refl/ qed-.
53
54 lemma aaa_reqg_conf (S) (G) (T) (A):
55       reflexive … S →
56       ∀L1. ❨G,L1❩ ⊢ T ⁝ A → ∀L2. L1 ≛[S,T] L2 → ❨G,L2❩ ⊢ T ⁝ A.
57 /3 width=7 by aaa_teqg_conf_reqg, teqg_refl/ qed-.