]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cnv_cpmue.etc
update in static_2 and basic_2 for the article
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / cpue / cnv_cpmue.etc
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/rt_computation/cpms_cnu.ma".
16 include "basic_2/rt_computation/cpmue.ma".
17 include "basic_2/dynamic/cnv_preserve.ma".
18
19 (* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
20
21 (* Properties with evaluation for t-unbound rt-transition on terms **********)
22
23 lemma cnv_cpmue_trans (a) (h) (G) (L):
24       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
25       ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
26 /3 width=4 by cpmue_fwd_cpms, cnv_cpms_trans/ qed-.
27
28 lemma cnv_cpmue_cpms_conf (a) (h) (G) (L):
29       ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[n1,h] T1 →
30       ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ →
31       ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[h,n2-n1] 𝐍*⦃T⦄ & T2 ≅ T.
32 #a #h #G #L #T0 #HT0 #T1 #n1 #HT01 #T2 #n2 * #HT02 #HT2
33 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
34 lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
35 /4 width=8 by cpmue_intro, cnu_tueq_trans, ex2_intro/
36 qed-.
37
38 (* Main properties with evaluation for t-unbound rt-transition on terms *****)
39
40 theorem cnv_cpmue_mono (a) (h) (G) (L):
41         ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[h,n1] 𝐍*⦃T1⦄ →
42         ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ → T1 ≅ T2.
43 #a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
44 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
45 /3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/
46 qed-.