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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "logic/equality.ma".
16 include "nat/compare.ma".
17 include "list/list.ma".
20 (*** useful definitions and lemmas not really related to Fsub ***)
26 |false \Rightarrow m].
28 lemma le_n_max_m_n: \forall m,n:nat. n \le max m n.
32 [simplify.intros.apply le_n
33 |simplify.intros.autobatch
37 lemma le_m_max_m_n: \forall m,n:nat. m \le max m n.
41 [simplify.intro.assumption
42 |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 }.
52 interpretation "item in list" 'mem x l = (in_list ? 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;