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/rt_computation/cnuw.ma".
16 include "basic_2/rt_computation/cprs_tweq.ma".
17 include "basic_2/rt_computation/lprs_cpms.ma".
19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
21 (* Advanced inversion lemmas ************************************************)
23 lemma cnuw_inv_abbr_pos (h) (G) (L):
24 ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
26 elim (cprs_abbr_pos_twneq h G L V T1) #T2 #HT12 #HnT12
30 (* Advanced properties ******************************************************)
32 lemma cnuw_abbr_neg (h) (G) (L): ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
33 #h #G #L #V1 #T1 #n #X #H
34 elim (cpms_inv_abbr_sn_dx … H) -H *
35 [ #V2 #T2 #_ #_ #H destruct /1 width=1 by tweq_abbr_neg/
36 | #X1 #_ #_ #H destruct
40 lemma cnuw_abst (h) (p) (G) (L): ∀W,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓛ{p}W.T.
41 #h #p #G #L #W1 #T1 #n #X #H
42 elim (cpms_inv_abst_sn … H) -H #W2 #T2 #_ #_ #H destruct
43 /1 width=1 by tweq_abst/
46 lemma cnuw_cpms_trans (h) (n) (G) (L):
47 ∀T1. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T1 →
48 ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T2.
49 #h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
50 /4 width=5 by cpms_trans, tweq_canc_sn/