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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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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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13 (**************************************************************************)
14
15 include "static_2/s_computation/fqus_fqup.ma".
16 include "basic_2/dynamic/cnv_drops.ma".
17
18 (* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
19
20 (* Properties with supclosure ***********************************************)
21
22 (* Basic_2A1: uses: snv_fqu_conf *)
23 lemma cnv_fqu_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
24                             ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
25 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
26 [ #I1 #G1 #L1 #V1 #H
27   elim (cnv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
28 | * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
29   [ elim (cnv_inv_bind … H) -H //
30   | elim (cnv_inv_appl … H) -H //
31   | elim (cnv_inv_cast … H) -H //
32   ]
33 | #p #I1 #G1 #L1 #V1 #T1 #H
34   elim (cnv_inv_bind … H) -H //
35 | #p #I1 #G1 #L1 #V1 #T1 #H destruct
36 | * #G1 #L1 #V1 #T1 #H
37   [ elim (cnv_inv_appl … H) -H //
38   | elim (cnv_inv_cast … H) -H //
39   ]
40 | #I1 #G1 #L1 #T1 #U1 #HTU1 #HU 
41   /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
42 ]
43 qed-.
44
45 (* Basic_2A1: uses: snv_fquq_conf *)
46 lemma cnv_fquq_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
47                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
48 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
49 /2 width=5 by cnv_fqu_conf/
50 qed-.
51
52 (* Basic_2A1: uses: snv_fqup_conf *)
53 lemma cnv_fqup_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
54                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
55 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
56 /3 width=5 by fqup_strap1, cnv_fqu_conf/
57 qed-.
58
59 (* Basic_2A1: uses: snv_fqus_conf *)
60 lemma cnv_fqus_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
61                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
62 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
63 /2 width=5 by cnv_fqup_conf/
64 qed-.