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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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15 include "basic_2/relocation/ldrop_lpx_sn.ma".
16 include "basic_2/reduction/cpx_lift.ma".
17 include "basic_2/reduction/lpx.ma".
19 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
21 (* Properies on local environment slicing ***********************************)
23 lemma lpx_ldrop_conf: ∀h,g,G. dropable_sn (lpx h g G).
24 /3 width=5 by lpx_sn_deliftable_dropable, cpx_inv_lift1/ qed-.
26 lemma ldrop_lpx_trans: ∀h,g,G. dedropable_sn (lpx h g G).
27 /3 width=9 by lpx_sn_liftable_dedropable, cpx_lift/ qed-.
29 lemma lpx_ldrop_trans_O1: ∀h,g,G. dropable_dx (lpx h g G).
30 /2 width=3 by lpx_sn_dropable/ qed-.
32 (* Properties on supclosure *************************************************)
34 lemma fsupq_lpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
35 ∀K2. ⦃G2, L2⦄ ⊢ ➡[h, g] K2 →
36 ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h, g] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T & ⦃G1, K1, T⦄ ⊃⸮ ⦃G2, K2, T2⦄.
37 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
38 /3 width=5 by fsup_fsupq, fsupq_refl, lpx_pair, fsup_lref_O, fsup_pair_sn, fsup_flat_dx, ex3_2_intro/
39 [ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpx_inv_pair1 … H) -H
40 #K2 #W2 #HLK2 #HVW2 #H destruct
41 /3 width=5 by fsup_fsupq, cpx_pair_sn, fsup_bind_dx, ex3_2_intro/
42 | #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IH12 #K0 #HK20
43 elim (IH12 … HK20) -K2 #K2 #T #HK12
44 elim (ldrop_lpx_trans … HLK1 … HK12) -HK12
45 elim (lift_total T d e)
46 /3 width=11 by cpx_lift, fsupq_ldrop, ex3_2_intro/