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/syntax/tueq.ma".
16 include "static_2/relocation/lifts_lifts.ma".
18 (* GENERIC RELOCATION FOR TERMS *********************************************)
20 (* Properties with tail sort-irrelevant equivalence for terms ***************)
22 lemma tueq_lifts_sn: liftable2_sn tueq.
23 #T1 #T2 #H elim H -T1 -T2
24 [ #s1 #s2 #f #X #H >(lifts_inv_sort1 … H) -H
25 /3 width=3 by lifts_sort, tueq_sort, ex2_intro/
26 | #i #f #X #H elim (lifts_inv_lref1 … H) -H
27 /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
28 | #l #f #X #H >(lifts_inv_gref1 … H) -H
29 /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
30 | #p #I #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_bind1 … H) -H
31 #W1 #U1 #HVW1 #HTU1 #H destruct
33 /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
34 | #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
35 #W1 #U1 #HVW1 #HTU1 #H destruct
37 /3 width=3 by lifts_flat, tueq_appl, ex2_intro/
38 | #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
39 #W1 #U1 #HVW1 #HTU1 #H destruct
40 elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
41 /3 width=5 by lifts_flat, tueq_cast, ex2_intro/
45 lemma tueq_lifts_dx: liftable2_dx tueq.
46 /3 width=3 by tueq_lifts_sn, liftable2_sn_dx, tueq_sym/ qed-.
48 lemma tueq_lifts_bi: liftable2_bi tueq.
49 /3 width=6 by tueq_lifts_sn, liftable2_sn_bi/ qed-.
51 (* Inversion lemmas with tail sort-irrelevant equivalence for terms *********)
53 lemma tueq_inv_lifts_sn: deliftable2_sn tueq.
54 #U1 #U2 #H elim H -U1 -U2
55 [ #s1 #s2 #f #X #H >(lifts_inv_sort2 … H) -H
56 /3 width=3 by lifts_sort, tueq_sort, ex2_intro/
57 | #i #f #X #H elim (lifts_inv_lref2 … H) -H
58 /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
59 | #l #f #X #H >(lifts_inv_gref2 … H) -H
60 /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
61 | #p #I #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_bind2 … H) -H
62 #V1 #T1 #HVW1 #HTU1 #H destruct
64 /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
65 | #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
66 #V1 #T1 #HVW1 #HTU1 #H destruct
68 /3 width=3 by lifts_flat, tueq_appl, ex2_intro/
69 | #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
70 #V1 #T1 #HVW1 #HTU1 #H destruct
71 elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
72 /3 width=5 by lifts_flat, tueq_cast, ex2_intro/
76 lemma tueq_inv_lifts_dx: deliftable2_dx tueq.
77 /3 width=3 by tueq_inv_lifts_sn, deliftable2_sn_dx, tueq_sym/ qed-.
79 lemma tueq_inv_lifts_bi: deliftable2_bi tueq.
80 /3 width=6 by tueq_inv_lifts_sn, deliftable2_sn_bi/ qed-.