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 "basic_2/static/ssta_lift.ma".
16 include "basic_2/static/ssta_ssta.ma".
17 include "basic_2/static/lsubss_ldrop.ma".
19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED STATIC TYPE ASSIGNMENT *******)
21 (* Properties concerning stratified native type assignment ******************)
23 lemma lsubss_ssta_trans: ∀h,g,L2,T,U,l. ⦃h, L2⦄ ⊢ T •[g,l] U →
24 ∀L1. h ⊢ L1 •⊑[g] L2 → ⦃h, L1⦄ ⊢ T •[g,l] U.
25 #h #g #L2 #T #U #l #H elim H -L2 -T -U -l
27 | #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
28 elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
29 elim (lsubss_inv_pair2 … H) -H * #K1 [ | -HWU2 -IHVW2 -HLK1 ]
30 [ #HK12 #H destruct /3 width=6/
31 | #V1 #l0 #_ #_ #_ #_ #H destruct
33 | #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #HWV2 #HWU2 #IHWV2 #L1 #HL12
34 elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
35 elim (lsubss_inv_pair2 … H) -H * #K1 [ -HWV2 | -IHWV2 ]
36 [ #HK12 #H destruct /3 width=6/
37 | #V1 #l0 #H1 #H2 #_ #H #_ destruct
38 elim (ssta_fwd_correct … H2) -H2 #V #H
39 elim (ssta_mono … HWV2 … H) -HWV2 -H /2 width=6/
47 lemma lsubss_ssta_conf: ∀h,g,L1,T,U,l. ⦃h, L1⦄ ⊢ T •[g,l] U →
48 ∀L2. h ⊢ L1 •⊑[g] L2 → ⦃h, L2⦄ ⊢ T •[g,l] U.
49 #h #g #L1 #T #U #l #H elim H -L1 -T -U -l
51 | #L1 #K1 #V1 #W1 #U1 #i #l #HLK1 #HVW1 #HWU1 #IHVW1 #L2 #HL12
52 elim (lsubss_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
53 elim (lsubss_inv_pair1 … H) -H * #K2 [ -HVW1 | -IHVW1 ]
54 [ #HK12 #H destruct /3 width=6/
55 | #V2 #l0 #H1 #H2 #_ #H #_ destruct
56 elim (ssta_mono … HVW1 … H1) -HVW1 -H1 #H1 #H2 destruct
57 elim (ssta_fwd_correct … H2) -H2 /2 width=6/
59 | #L1 #K1 #W1 #V1 #U1 #i #l #HLK1 #_ #HWU1 #IHWV1 #L2 #HL12
60 elim (lsubss_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
61 elim (lsubss_inv_pair1 … H) -H * #K2 [ | -HWU1 -IHWV1 -HLK2 ]
62 [ #HK12 #H destruct /3 width=6/
63 | #V2 #l0 #_ #_ #_ #_ #H destruct