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 "basic_2/dynamic/nta_cpcs.ma".
16 include "basic_2/dynamic/nta_preserve.ma".
18 (* NATIVE TYPE ASSIGNMENT FOR TERMS ****************************************)
20 (* Properties based on type equivalence and preservation *******************)
22 (* Basic_1: uses: ty3_tred *)
23 lemma nta_cprs_trans (h) (a) (G) (L):
24 ∀T,U1. ❨G,L❩ ⊢ T :[h,a] U1 → ∀U2. ❨G,L❩ ⊢ U1 ➡*[h,0] U2 → ❨G,L❩ ⊢ T :[h,a] U2.
25 #h #a #G #L #T #U1 #H #U2 #HU12
26 /4 width=4 by nta_conv_cnv, nta_fwd_cnv_dx, cnv_cpms_trans, cpcs_cprs_dx/
29 (* Basic_1: uses: ty3_sred_back *)
30 lemma cprs_nta_trans (h) (a) (G) (L):
31 ∀T1,U0. ❨G,L❩ ⊢ T1 :[h,a] U0 → ∀T2. ❨G,L❩ ⊢ T1 ➡*[h,0] T2 →
32 ∀U. ❨G,L❩ ⊢ T2 :[h,a] U → ❨G,L❩ ⊢ T1 :[h,a] U.
33 #h #a #G #L #T1 #U0 #HT1 #T2 #HT12 #U #H
34 lapply (nta_cprs_conf … HT1 … HT12) -HT12 #HT2
35 /4 width=6 by nta_mono, nta_conv_cnv, nta_fwd_cnv_dx/
38 lemma cprs_nta_trans_cnv (h) (a) (G) (L):
39 ∀T1. ❨G,L❩ ⊢ T1 ![h,a] → ∀T2. ❨G,L❩ ⊢ T1 ➡*[h,0] T2 →
40 ∀U. ❨G,L❩ ⊢ T2 :[h,a] U → ❨G,L❩ ⊢ T1 :[h,a] U.
41 #h #a #G #L #T1 #HT1 #T2 #HT12 #U #H
42 elim (cnv_nta_sn … HT1) -HT1 #U0 #HT1
43 /2 width=3 by cprs_nta_trans/
46 (* Basic_1: uses: ty3_sconv *)
47 lemma nta_cpcs_conf (h) (a) (G) (L):
48 ∀T1,U. ❨G,L❩ ⊢ T1 :[h,a] U → ∀T2. ❨G,L❩ ⊢ T1 ⬌*[h] T2 →
49 ∀U0. ❨G,L❩ ⊢ T2 :[h,a] U0 → ❨G,L❩ ⊢ T2 :[h,a] U.
50 #h #a #G #L #T1 #U #HT1 #T2 #HT12 #U0 #HT2
51 elim (cpcs_inv_cprs … HT12) -HT12 #T0 #HT10 #HT02
52 /3 width=5 by cprs_nta_trans, nta_cprs_conf/
55 (* Note: type preservation by valid r-equivalence *)
56 lemma nta_cpcs_conf_cnv (h) (a) (G) (L):
57 ∀T1,U. ❨G,L❩ ⊢ T1 :[h,a] U →
58 ∀T2. ❨G,L❩ ⊢ T1 ⬌*[h] T2 → ❨G,L❩ ⊢ T2 ![h,a] → ❨G,L❩ ⊢ T2 :[h,a] U.
59 #h #a #G #L #T1 #U #HT1 #T2 #HT12 #HT2
60 elim (cnv_nta_sn … HT2) -HT2 #U0 #HT2
61 /2 width=3 by nta_cpcs_conf/