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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "static_2/syntax/tweq_simple.ma".
16 include "basic_2/rt_computation/cpms_cpms.ma".
17 include "basic_2/rt_computation/cnuw.ma".
19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
21 (* Advanced forward lemma with with simple terms ****************************)
23 lemma cnuw_fwd_appl_simple (h) (G) (L):
24 ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T → 𝐒⦃T⦄.
26 elim (simple_dec_ex T) [ // ] * #p #I #W #U #H destruct
28 (* Advanced properties with simple terms ************************************)
30 lemma cnuw_appl_simple (h) (G) (L):
31 ∀V,T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T.
32 #h #G #L #V1 #T1 #H1T1 #H2T1 #n #X #H
33 elim (cpms_inv_appl_sn … H) -H *
34 [ #V2 #T2 #_ #HT12 #H destruct -H1T1
35 /3 width=2 by tweq_appl/
36 | #n1 #n2 #p #V2 #T2 #HT12 #_ #_ -n -n2
37 lapply (H2T1 … HT12) -H2T1 -n1 #H
38 lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
39 elim (simple_inv_bind … H)
40 | #n1 #n2 #p #V2 #W2 #W #T2 #_ #_ #HT12 #_ #_ -n -n2 -V2 -W2
41 lapply (H2T1 … HT12) -H2T1 -n1 #H
42 lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
43 elim (simple_inv_bind … H)