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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 "static_2/relocation/lifts_teqx.ma".
16 include "basic_2/rt_transition/cpx_drops.ma".
17 include "basic_2/rt_transition/cnx.ma".
19 (* NORMAL TERMS FOR EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION *******)
21 (* Properties with generic slicing ******************************************)
23 lemma cnx_lref_atom (G) (L):
24 ∀i. ⇩[i] L ≘ ⋆ → ❪G,L❫ ⊢ ⬈𝐍 #i.
25 #G #L #i #Hi #X #H elim (cpx_inv_lref1_drops … H) -H // *
26 #I #K #V1 #V2 #HLK lapply (drops_mono … Hi … HLK) -L #H destruct
29 lemma cnx_lref_unit (G) (L):
30 ∀I,K,i. ⇩[i] L ≘ K.ⓤ[I] → ❪G,L❫ ⊢ ⬈𝐍 #i.
31 #G #L #I #K #i #HLK #X #H elim (cpx_inv_lref1_drops … H) -H // *
32 #Z #Y #V1 #V2 #HLY lapply (drops_mono … HLK … HLY) -L #H destruct
35 (* Basic_2A1: includes: cnx_lift *)
36 lemma cnx_lifts (G): d_liftable1 … (cnx G).
37 #G #K #T #HT #b #f #L #HLK #U #HTU #U0 #H
38 elim (cpx_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
39 lapply (HT … HT0) -G -K /2 width=6 by teqx_lifts_bi/
42 (* Inversion lemmas with generic slicing ************************************)
44 (* Basic_2A1: was: cnx_inv_delta *)
45 lemma cnx_inv_lref_pair (G) (L):
46 ∀I,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,L❫ ⊢ ⬈𝐍 #i → ⊥.
47 #G #L #I #K #V #i #HLK #H
48 elim (lifts_total V (𝐔❨↑i❩)) #W #HVW
49 lapply (H W ?) -H /2 width=7 by cpx_delta_drops/ -HLK
50 #H lapply (teqg_inv_lref1 … H) -H #H destruct
51 /2 width=5 by lifts_inv_lref2_uni_lt/
54 (* Basic_2A1: includes: cnx_inv_lift *)
55 lemma cnx_inv_lifts (G): d_deliftable1 … (cnx G).
56 #G #L #U #HU #b #f #K #HLK #T #HTU #T0 #H
57 elim (cpx_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
58 lapply (HU … HU0) -G -L /2 width=6 by teqx_inv_lifts_bi/