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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 "basic_2/rt_computation/cprs_cnr.ma".
16 include "basic_2/rt_computation/cprre.ma".
17 include "basic_2/dynamic/cnv_preserve.ma".
19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
21 (* Properties with t-bound evaluation on terms ******************************)
23 lemma cnv_cpmre_trans (h) (a) (n) (G) (L):
24 ∀T1. ❨G,L❩ ⊢ T1 ![h,a] →
25 ∀T2. ❨G,L❩ ⊢ T1 ➡*𝐍[h,n] T2 → ❨G,L❩ ⊢ T2 ![h,a].
26 #h #a #n #G #L #T1 #HT1 #T2 * #HT12 #_
27 /2 width=4 by cnv_cpms_trans/
30 lemma cnv_cpmre_cpms_conf (h) (a) (n) (G) (L):
31 ∀T. ❨G,L❩ ⊢ T ![h,a] → ∀T1. ❨G,L❩ ⊢ T ➡*[h,n] T1 →
32 ∀T2. ❨G,L❩ ⊢ T ➡*𝐍[h,n] T2 → ❨G,L❩ ⊢ T1 ➡*𝐍[h,0] T2.
33 #h #a #n #G #L #T0 #HT0 #T1 #HT01 #T2 * #HT02 #HT2
34 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 <minus_n_n #T0 #HT10 #HT20
35 lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
36 /2 width=1 by cpmre_intro/
39 (* Main properties with evaluation for t-bound rt-transition on terms *****)
41 theorem cnv_cpmre_mono (h) (a) (n) (G) (L):
42 ∀T. ❨G,L❩ ⊢ T ![h,a] → ∀T1. ❨G,L❩ ⊢ T ➡*𝐍[h,n] T1 →
43 ∀T2. ❨G,L❩ ⊢ T ➡*𝐍[h,n] T2 → T1 = T2.
44 #h #a #n #G #L #T0 #HT0 #T1 * #HT01 #HT1 #T2 * #HT02 #HT2
45 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 <minus_n_n #T0 #HT10 #HT20
46 /3 width=7 by cprs_inv_cnr_sn, canc_dx_eq/