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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/substitution/lpss_cpss.ma".
17 (* SN PARALLEL SUBSTITUTION ON LOCAL ENVIRONMENTS ***************************)
19 (* Main properties **********************************************************)
21 theorem lpss_conf: confluent … lpss.
22 /3 width=6 by lpx_sn_conf, cpss_conf_lpss/
25 theorem lpss_trans: Transitive … lpss.
26 /3 width=5 by lpx_sn_trans, cpss_trans_lpss/
29 (* Advanced forward lemmas **************************************************)
31 lemma cpss_fwd_shift1: ∀L1,L,T1,T. L ⊢ L1 @@ T1 ▶* T →
32 ∃∃L2,T2. L @@ L1 ⊢ ▶* L @@ L2 & L @@ L1 ⊢ T1 ▶* T2 &
34 #L1 @(lenv_ind_dx … L1) -L1
36 @ex3_2_intro [3: // |4,5: // |1,2: skip ] (**) (* /2 width=4/ does not work *)
37 | #I #L1 #V1 #IH #L #T1 #T >shift_append_assoc #H <append_assoc
38 elim (cpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
39 elim (IH … HT12) -IH -HT12 #L2 #T #HL12 #HT1 #H destruct
40 lapply (lpss_trans … HL12 (L.ⓑ{I}V2@@L2) ?) -HL12 /3 width=1/ #HL12
41 @(ex3_2_intro … (⋆.ⓑ{I}V2@@L2)) [4: /2 width=3/ | skip ] <append_assoc // (**) (* explicit constructor *)