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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 "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 UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
21 (* Properties with generic slicing ******************************************)
23 lemma cnx_lref_atom: ∀h,G,L,i. ⇩*[i] L ≘ ⋆ → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
24 #h #G #L #i #Hi #X #H elim (cpx_inv_lref1_drops … H) -H // *
25 #I #K #V1 #V2 #HLK lapply (drops_mono … Hi … HLK) -L #H destruct
28 lemma cnx_lref_unit: ∀h,I,G,L,K,i. ⇩*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
29 #h #I #G #L #K #i #HLK #X #H elim (cpx_inv_lref1_drops … H) -H // *
30 #Z #Y #V1 #V2 #HLY lapply (drops_mono … HLK … HLY) -L #H destruct
33 (* Basic_2A1: includes: cnx_lift *)
34 lemma cnx_lifts: ∀h,G. d_liftable1 … (cnx h G).
35 #h #G #K #T #HT #b #f #L #HLK #U #HTU #U0 #H
36 elim (cpx_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
37 lapply (HT … HT0) -G -K /2 width=6 by teqx_lifts_bi/
40 (* Inversion lemmas with generic slicing ************************************)
42 (* Basic_2A1: was: cnx_inv_delta *)
43 lemma cnx_inv_lref_pair: ∀h,I,G,L,K,V,i. ⇩*[i] L ≘ K.ⓑ{I}V → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄ → ⊥.
44 #h #I #G #L #K #V #i #HLK #H
45 elim (lifts_total V (𝐔❴↑i❵)) #W #HVW
46 lapply (H W ?) -H /2 width=7 by cpx_delta_drops/ -HLK
47 #H lapply (teqx_inv_lref1 … H) -H #H destruct
48 /2 width=5 by lifts_inv_lref2_uni_lt/
51 (* Basic_2A1: includes: cnx_inv_lift *)
52 lemma cnx_inv_lifts: ∀h,G. d_deliftable1 … (cnx h G).
53 #h #G #L #U #HU #b #f #K #HLK #T #HTU #T0 #H
54 elim (cpx_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
55 lapply (HU … HU0) -G -L /2 width=6 by teqx_inv_lifts_bi/