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/s_computation/fqus_fqup.ma".
16 include "basic_2/dynamic/cnv_drops.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Properties with supclosure ***********************************************)
22 (* Basic_2A1: uses: snv_fqu_conf *)
23 lemma cnv_fqu_conf (h) (a):
24 ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂ ⦃G2,L2,T2⦄ →
25 ⦃G1,L1⦄ ⊢ T1 ![h,a] → ⦃G2,L2⦄ ⊢ T2 ![h,a].
26 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
28 elim (cnv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
29 | * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
30 [ elim (cnv_inv_bind … H) -H //
31 | elim (cnv_inv_appl … H) -H //
32 | elim (cnv_inv_cast … H) -H //
34 | #p #I1 #G1 #L1 #V1 #T1 #_ #H
35 elim (cnv_inv_bind … H) -H //
36 | #p #I1 #G1 #L1 #V1 #T1 #H destruct
37 | * #G1 #L1 #V1 #T1 #H
38 [ elim (cnv_inv_appl … H) -H //
39 | elim (cnv_inv_cast … H) -H //
41 | #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
42 /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
46 (* Basic_2A1: uses: snv_fquq_conf *)
47 lemma cnv_fquq_conf (h) (a):
48 ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂⸮ ⦃G2,L2,T2⦄ →
49 ⦃G1,L1⦄ ⊢ T1 ![h,a] → ⦃G2,L2⦄ ⊢ T2 ![h,a].
50 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
51 /2 width=5 by cnv_fqu_conf/
54 (* Basic_2A1: uses: snv_fqup_conf *)
55 lemma cnv_fqup_conf (h) (a):
56 ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+ ⦃G2,L2,T2⦄ →
57 ⦃G1,L1⦄ ⊢ T1 ![h,a] → ⦃G2,L2⦄ ⊢ T2 ![h,a].
58 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
59 /3 width=5 by fqup_strap1, cnv_fqu_conf/
62 (* Basic_2A1: uses: snv_fqus_conf *)
63 lemma cnv_fqus_conf (h) (a):
64 ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂* ⦃G2,L2,T2⦄ →
65 ⦃G1,L1⦄ ⊢ T1 ![h,a] → ⦃G2,L2⦄ ⊢ T2 ![h,a].
66 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
67 /2 width=5 by cnv_fqup_conf/