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 *)
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15 include "basic_2/static/frees_fqup.ma".
16 include "basic_2/static/lfxs.ma".
18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
20 (* Advanced properties ******************************************************)
22 lemma lfxs_refl: ∀R. (∀L. reflexive … (R L)) → ∀L,T. L ⦻*[R, T] L.
23 #R #HR #L #T elim (frees_total L T) /3 width=3 by lexs_refl, ex2_intro/
26 lemma lfxs_pair: ∀R. (∀L. reflexive … (R L)) →
27 ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⦻*[R, T] L.ⓑ{I}V2.
28 #R #HR #L #V1 #V2 #HV12 #I #T
29 elim (frees_total (L.ⓑ{I}V1) T) #f #Hf
30 elim (pn_split f) * #g #H destruct
31 /4 width=3 by lexs_refl, lexs_next, lexs_push, ex2_intro/