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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/rt_transition/cpr_drops.ma".
16 include "basic_2/rt_transition/cnr.ma".
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE R-TRANSITION **************************)
20 (* Advanced properties ******************************************************)
22 (* Basic_1: was only: nf2_csort_lref *)
23 lemma cnr_lref_atom (h) (b) (G) (L):
24 ∀i. ⇩*[b,𝐔❨i❩] L ≘ ⋆ → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫.
25 #h #b #G #L #i #Hi #X #H
26 elim (cpr_inv_lref1_drops … H) -H // * #K #V1 #V2 #HLK
27 lapply (drops_gen b … HLK) -HLK #HLK
28 lapply (drops_mono … Hi … HLK) -L #H destruct
31 (* Basic_1: was: nf2_lref_abst *)
32 lemma cnr_lref_abst (h) (G) (L):
33 ∀K,V,i. ⇩*[i] L ≘ K.ⓛV → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫.
34 #h #G #L #K #V #i #HLK #X #H
35 elim (cpr_inv_lref1_drops … H) -H // *
36 #K0 #V1 #V2 #HLK0 #_ #_
37 lapply (drops_mono … HLK … HLK0) -L #H destruct
40 lemma cnr_lref_unit (h) (I) (G) (L):
41 ∀K,i. ⇩*[i] L ≘ K.ⓤ[I] → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫.
42 #h #I #G #L #K #i #HLK #X #H
43 elim (cpr_inv_lref1_drops … H) -H // *
44 #K0 #V1 #V2 #HLK0 #_ #_
45 lapply (drops_mono … HLK … HLK0) -L #H destruct
48 (* Properties with generic relocation ***************************************)
50 (* Basic_1: was: nf2_lift *)
51 (* Basic_2A1: uses: cnr_lift *)
52 lemma cnr_lifts (h) (G): d_liftable1 … (cnr h G).
53 #h #G #K #T #HT #b #f #L #HLK #U #HTU #U0 #H
54 elim (cpm_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
55 lapply (HT … HT0) -G -K #H destruct /2 width=4 by lifts_mono/
58 (* Advanced inversion lemmas ************************************************)
60 (* Basic_2A1: was: cnr_inv_delta *)
61 lemma cnr_inv_lref_abbr (h) (G) (L):
62 ∀K,V,i. ⇩*[i] L ≘ K.ⓓV → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫ → ⊥.
63 #h #G #L #K #V #i #HLK #H
64 elim (lifts_total V 𝐔❨↑i❩) #W #HVW
65 lapply (H W ?) -H [ /3 width=6 by cpm_delta_drops/ ] -HLK #H destruct
66 elim (lifts_inv_lref2_uni_lt … HVW) -HVW //
69 (* Inversion lemmas with generic relocation *********************************)
71 (* Note: this was missing in Basic_1 *)
72 (* Basic_2A1: uses: cnr_inv_lift *)
73 lemma cnr_inv_lifts (h) (G): d_deliftable1 … (cnr h G).
74 #h #G #L #U #HU #b #f #K #HLK #T #HTU #T0 #H
75 elim (cpm_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
76 lapply (HU … HU0) -G -L #H destruct /2 width=4 by lifts_inj/