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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/multiple/llpx_sn_drop.ma".
16 include "basic_2/unfold/lstas.ma".
18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
20 (* Properties on lazy sn pointwise extensions *******************************)
22 lemma lstas_llpx_sn_conf: ∀R. (∀L. reflexive … (R L)) → d_liftable R →
23 ∀h,G,d. c_r_confluent1 … (lstas h d G) (llpx_sn R 0).
24 #R #H1R #H2R #h #G #d #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2 -d
25 [ /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
26 | #G #Ls #Ks #V1c #V2c #W2c #i #d #HLKs #_ #HVW2c #IHV12c #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
27 #Kd #V1l #HLKd #HV1c #HV1sd
28 lapply (drop_fwd_drop2 … HLKs) -HLKs #HLKs
29 lapply (drop_fwd_drop2 … HLKd) -HLKd #HLKd
30 @(llpx_sn_lift_le … HLKs HLKd … HVW2c) -HLKs -HLKd -HVW2c /2 width=1 by/ (**) (* full auto too slow *)
32 | #G #Ls #Ks #V1c #V2c #W2c #i #d #HLKs #_ #HVW2c #IHV12c #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
33 #Kd #V1l #HLKd #HV1c #HV1sd
34 lapply (drop_fwd_drop2 … HLKs) -HLKs #HLKs
35 lapply (drop_fwd_drop2 … HLKd) -HLKd #HLKd
36 @(llpx_sn_lift_le … HLKs HLKd … HVW2c) -HLKs -HLKd -HVW2c /2 width=1 by/ (**) (* full auto too slow *)
37 | #a #I #G #Ls #V #T1 #T2 #d #_ #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 #d #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
40 /3 width=1 by llpx_sn_flat/
41 | #G #Ls #V #T1 #T2 #d #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
42 /3 width=1 by llpx_sn_flat/