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 *)
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15 include "static_2/syntax/tdeq.ma".
16 include "static_2/relocation/lifts_lifts.ma".
18 (* GENERIC RELOCATION FOR TERMS *********************************************)
20 (* Properties with sort-irrelevant equivalence for terms ********************)
22 lemma tdeq_lifts_sn: liftable2_sn tdeq.
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, tdeq_sort, ex2_intro/
26 | #i #f #X #H elim (lifts_inv_lref1 … H) -H
27 /3 width=3 by lifts_lref, tdeq_lref, ex2_intro/
28 | #l #f #X #H >(lifts_inv_gref1 … H) -H
29 /2 width=3 by lifts_gref, tdeq_gref, ex2_intro/
30 | #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_bind1 … H) -H
31 #W1 #U1 #HVW1 #HTU1 #H destruct
32 elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
33 /3 width=5 by lifts_bind, tdeq_pair, ex2_intro/
34 | #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
35 #W1 #U1 #HVW1 #HTU1 #H destruct
36 elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
37 /3 width=5 by lifts_flat, tdeq_pair, ex2_intro/
41 lemma tdeq_lifts_bi: liftable2_bi tdeq.
42 /3 width=6 by tdeq_lifts_sn, liftable2_sn_bi/ qed-.
44 (* Inversion lemmas with sort-irrelevant equivalence for terms **************)
46 lemma tdeq_inv_lifts_sn: deliftable2_sn tdeq.
47 #U1 #U2 #H elim H -U1 -U2 [||| * ]
48 [ #s1 #s2 #f #X #H >(lifts_inv_sort2 … H) -H
49 /3 width=3 by lifts_sort, tdeq_sort, ex2_intro/
50 | #i #f #X #H elim (lifts_inv_lref2 … H) -H
51 /3 width=3 by lifts_lref, tdeq_lref, ex2_intro/
52 | #l #f #X #H >(lifts_inv_gref2 … H) -H
53 /2 width=3 by lifts_gref, tdeq_gref, ex2_intro/
54 | #p #I #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_bind2 … H) -H
55 #V1 #T1 #HVW1 #HTU1 #H destruct
56 elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
57 /3 width=5 by lifts_bind, tdeq_pair, ex2_intro/
58 | #I #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
59 #V1 #T1 #HVW1 #HTU1 #H destruct
60 elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
61 /3 width=5 by lifts_flat, tdeq_pair, ex2_intro/
65 lemma tdeq_inv_lifts_dx: deliftable2_dx tdeq.
66 /3 width=3 by tdeq_inv_lifts_sn, deliftable2_sn_dx, tdeq_sym/ qed-.
68 lemma tdeq_inv_lifts_bi: deliftable2_bi tdeq.
69 /3 width=6 by tdeq_inv_lifts_sn, deliftable2_sn_bi/ qed-.
71 lemma tdeq_lifts_inv_pair_sn (I) (f:rtmap):
72 ∀X,T. ⬆*[f]X ≘ T → ∀V. ②{I}V.T ≛ X → ⊥.
73 #I #f #X #T #H elim H -f -X -T
75 elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
77 elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
79 elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
80 | #f #p #J #X1 #T1 #X2 #T2 #_ #_ #_ #IH2 #V #H
81 elim (tdeq_inv_pair1 … H) -H #Z1 #Z2 #_ #HZ2 #H destruct
83 | #f #J #X1 #T1 #X2 #T2 #_ #_ #_ #IH2 #V #H
84 elim (tdeq_inv_pair1 … H) -H #Z1 #Z2 #_ #HZ2 #H destruct