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/relocation/llpx_sn_ldrop.ma".
16 include "basic_2/static/ssta.ma".
18 (* STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS ******************************)
20 (* Properties on lazy sn pointwise extensions *******************************)
22 lemma ssta_llpx_sn_conf: ∀R. (∀I,L.reflexive … (R I L)) →
23 (∀I.l_liftable (R I)) →
24 ∀h,g,G. s_r_confluent1 … (ssta h g G) (llpx_sn R 0).
25 #R #H1R #H2R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
26 [ /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
27 | #G #Ls #Ks #V1s #W2s #V2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
28 #Kd #V1d #HLKd #HV1s #HV1sd
29 lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
30 lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
31 @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
32 | #G #Ls #Ks #V1s #W1s #l #i #HLKs #Hl #HVW1s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
33 #Kd #V1d #HLKd #HV1s #HV1sd
34 lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
35 lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
36 @(llpx_sn_lift_le … HLKs HLKd … HVW1s) -HLKs -HLKd -HVW1s /2 width=1 by/ (**) (* full auto too slow *)
37 | #a #I #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
38 /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
39 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
40 /3 width=1 by llpx_sn_flat/
41 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
42 /3 width=1 by llpx_sn_flat/