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 set "baseuri" "cic:/matita/Fsub/util".
16 include "logic/equality.ma".
17 include "nat/compare.ma".
18 include "list/list.ma".
21 (*** useful definitions and lemmas not really related to Fsub ***)
27 |false \Rightarrow m].
29 lemma le_n_max_m_n: \forall m,n:nat. n \le max m n.
33 [simplify.intros.apply le_n
34 |simplify.intros.autobatch
38 lemma le_m_max_m_n: \forall m,n:nat. m \le max m n.
42 [simplify.intro.assumption
43 |simplify.intros.autobatch
47 notation > "hvbox(x ∈ l)"
48 non associative with precedence 30 for @{ 'inlist $x $l }.
49 notation < "hvbox(x \nbsp ∈ \nbsp l)"
50 non associative with precedence 30 for @{ 'inlist $x $l }.
51 interpretation "item in list" 'inlist x l =
52 (cic:/matita/list/in/in_list.ind#xpointer(1/1) _ x l).
54 lemma max_case : \forall m,n.(max m n) = match (leb m n) with
56 | false \Rightarrow m ].
57 intros;elim m;simplify;reflexivity;