1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 include "ground/xoa/ex_4_5.ma".
16 include "basic_2/rt_transition/cpg_drops.ma".
17 include "basic_2/rt_transition/cpx.ma".
19 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
21 (* Advanced properties ******************************************************)
23 (* Basic_2A1: was: cpx_delta *)
24 lemma cpx_delta_drops (G) (L):
26 ⇩[i] L ≘ K.ⓑ[I]V → ❨G,K❩ ⊢ V ⬈ V2 →
27 ⇧[↑i] V2 ≘ W2 → ❨G,L❩ ⊢ #i ⬈ W2.
28 #G #L * #K #V #V2 #W2 #i #HLK *
29 /3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
32 (* Advanced inversion lemmas ************************************************)
34 (* Basic_2A1: was: cpx_inv_atom1 *)
35 lemma cpx_inv_atom1_drops (G) (L):
36 ∀I,T2. ❨G,L❩ ⊢ ⓪[I] ⬈ T2 →
38 | ∃∃s1,s2. T2 = ⋆s2 & I = Sort s1
39 | ∃∃J,K,V,V2,i. ⇩[i] L ≘ K.ⓑ[J]V & ❨G,K❩ ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i.
40 #G #L #I #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
41 /4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_2_intro, ex_intro/
44 (* Basic_2A1: was: cpx_inv_lref1 *)
45 lemma cpx_inv_lref1_drops (G) (L):
46 ∀T2,i. ❨G,L❩ ⊢ #i ⬈ T2 →
48 | ∃∃J,K,V,V2. ⇩[i] L ≘ K. ⓑ[J]V & ❨G,K❩ ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2.
49 #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
50 /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
53 (* Properties with generic slicing for local environments *******************)
55 (* Basic_2A1: includes: cpx_lift *)
56 lemma cpx_lifts_sn (G): d_liftable2_sn … lifts (cpx G).
57 #G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
58 elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
59 /3 width=4 by ex2_intro, ex_intro/
62 lemma cpx_lifts_bi (G): d_liftable2_bi … lifts (cpx G).
63 #G #K #T1 #T2 * /3 width=10 by cpg_lifts_bi, ex_intro/
66 (* Inversion lemmas with generic slicing for local environments *************)
68 (* Basic_2A1: includes: cpx_inv_lift1 *)
69 lemma cpx_inv_lifts_sn (G): d_deliftable2_sn … lifts (cpx G).
70 #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
71 elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
72 /3 width=4 by ex2_intro, ex_intro/
75 lemma cpx_inv_lifts_bi (G): d_deliftable2_bi …lifts (cpx G).
76 #G #L #U1 #U2 * /3 width=10 by cpg_inv_lifts_bi, ex_intro/