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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 "ground_2/notation/functions/circledE_1.ma".
16 include "ground_2/notation/functions/oplusright_3.ma".
17 include "ground_2/lib/relations.ma".
19 (* LISTS ********************************************************************)
21 inductive list (A:Type[0]) : Type[0] :=
23 | cons: A → list A → list A.
25 interpretation "nil (list)" 'CircledE A = (nil A).
27 interpretation "cons (list)" 'OPlusRight A hd tl = (cons A hd tl).
29 rec definition all A (R:predicate A) (l:list A) on l ≝
32 | cons hd tl ⇒ ∧∧ R hd & all A R tl