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- extended multiple substitutions now uses bounds in ynat (ie. they
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14
15 include "basic_2/relocation/fsup.ma".
16 include "basic_2/relocation/ldrop_lpx_sn.ma".
17 include "basic_2/substitution/cpss_lift.ma".
18 include "basic_2/substitution/lpss.ma".
19
20 (* SN PARALLEL SUBSTITUTION FOR LOCAL ENVIRONMENTS **************************)
21
22 (* Properies on local environment slicing ***********************************)
23
24 lemma lpss_ldrop_conf: dropable_sn lpss.
25 /3 width=5 by lpx_sn_deliftable_dropable, cpss_inv_lift1/ qed-.
26
27 lemma ldrop_lpss_trans: dedropable_sn lpss.
28 /3 width=9 by lpx_sn_liftable_dedropable, cpss_lift/ qed-.
29
30 lemma lpss_ldrop_trans_O1: dropable_dx lpss.
31 /2 width=3 by lpx_sn_dropable/ qed-.
32
33 (* Properties on context-sensitive parallel substitution for terms **********)
34
35 lemma fsup_cpss_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ▶* U2 →
36                        ∃∃L,U1. L1 ⊢ ▶* L & L ⊢ T1 ▶* U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
37 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [2: * ] [1,2,3,4,5: /3 width=5/ ]
38 [ #L #K #U #T #d #e #HLK #HUT #He #U2 #HU2
39   elim (lift_total U2 d e) #T2 #HUT2
40   lapply (cpss_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9/
41 | #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
42   elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HT2
43   elim (lift_total T d e) #U #HTU
44   elim (ldrop_lpss_trans … HLK1 … HK1) -HLK1 -HK1 #L2 #HL12 #HL2K
45   lapply (cpss_lift … HT1 … HL2K … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
46 ]
47 qed-.