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/reducibility/cpr_cpr.ma".
16 include "basic_2/computation/csn.ma".
18 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
20 (* Advanced forvard lemmas **************************************************)
22 fact csn_fwd_pair_sn_aux: ∀L,U. L ⊢ ⬊* U → ∀I,V,T. U = ②{I} V. T → L ⊢ ⬊* V.
23 #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
24 @csn_intro #V2 #HLV2 #HV2
25 @(IH (②{I} V2. T)) -IH // /2 width=1/ -HLV2 #H destruct /2 width=1/
28 (* Basic_1: was: sn3_gen_head *)
29 lemma csn_fwd_pair_sn: ∀I,L,V,T. L ⊢ ⬊* ②{I} V. T → L ⊢ ⬊* V.
32 fact csn_fwd_bind_dx_aux: ∀L,U. L ⊢ ⬊* U →
33 ∀a,I,V,T. U = ⓑ{a,I} V. T → L. ⓑ{I} V ⊢ ⬊* T.
34 #L #U #H elim H -H #U0 #_ #IH #a #I #V #T #H destruct
35 @csn_intro #T2 #HLT2 #HT2
36 @(IH (ⓑ{a,I} V. T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
39 (* Basic_1: was: sn3_gen_bind *)
40 lemma csn_fwd_bind_dx: ∀a,I,L,V,T. L ⊢ ⬊* ⓑ{a,I} V. T → L. ⓑ{I} V ⊢ ⬊* T.