(**************************************************************************)
include "ground_2/notation/constructors/nil_0.ma".
-include "ground_2/notation/constructors/cons_2.ma".
+include "ground_2/notation/constructors/oplusright_3.ma".
include "ground_2/lib/arith.ma".
(* LISTS ********************************************************************)
interpretation "nil (list)" 'Nil = (nil ?).
-interpretation "cons (list)" 'Cons hd tl = (cons ? hd tl).
+interpretation "cons (list)" 'OPlusRight A hd tl = (cons A hd tl).
-rec definition length (A:Type[0]) (l:list A) on l ≝ match l with
+rec definition length A (l:list A) on l ≝ match l with
[ nil ⇒ 0
| cons _ l ⇒ ↑(length A l)
].
lemma length_nil (A:Type[0]): |nil A| = 0.
// qed.
-lemma length_cons (A:Type[0]) (l:list A) (a:A): |a@l| = ↑|l|.
+lemma length_cons (A:Type[0]) (l:list A) (a:A): |a⨮l| = ↑|l|.
// qed.
(* Basic inversion lemmas on length *****************************************)
/2 width=1 by length_inv_zero_dx/ qed-.
lemma length_inv_succ_dx (A:Type[0]) (l:list A) (x): |l| = ↑x →
- ∃∃tl,a. x = |tl| & l = a @ tl.
+ ∃∃tl,a. x = |tl| & l = a ⨮ tl.
#A * /2 width=4 by ex2_2_intro/
>length_nil #x #H destruct
qed-.
lemma length_inv_succ_sn (A:Type[0]) (l:list A) (x): ↑x = |l| →
- ∃∃tl,a. x = |tl| & l = a @ tl.
+ ∃∃tl,a. x = |tl| & l = a ⨮ tl.
/2 width=1 by length_inv_succ_dx/ qed.