Data.List1.Elem

Definitions

data Elem : a -> List1 a -> Type

  A proof that some element is found in a list.

Totality: total
Visibility: public export
Constructors:

Here : Elem x (x ::: xs)

  A proof that the element is at the head of the list

There : Elem x xs -> Elem x (y ::: xs)

  A proof that the element is in the tail of the list

Hints:

DecEq (Elem x xs)

Injective There

Uninhabited (Here = There e)

Uninhabited (There e = Here)

Uninhabited (x = z) => Uninhabited (Elem z xs) => Uninhabited (Elem z (x ::: xs))

neitherHereNorThere : Not (x = y) -> Not (Elem x xs) -> Not (Elem x (y ::: xs))

  An item not in the head and not in the tail is not in the list at all.

Totality: total
Visibility: export

isElem : DecEq a => (x : a) -> (xs : List1 a) -> Dec (Elem x xs)

  Check whether the given element is a member of the given list.

Totality: total
Visibility: public export

dropElem : (xs : List1 a) -> Elem x xs -> List a

  Remove the element at the given position. Forgets that the list is
  non-empty, since there is no guarantee that it will remain non-empty after
  the removal.

Totality: total
Visibility: public export

elemToNat : Elem x xs -> Nat

  Erase the indices, returning the numeric position of the element

Totality: total
Visibility: public export

indexElem : Nat -> (xs : List1 a) -> Maybe (x : a ** Elem x xs)

  Find the element with a proof at a given position, if it is valid

Totality: total
Visibility: public export

elemMap : (0 f : (a -> b)) -> Elem x xs -> Elem (f x) (map f xs)

  Lift the membership proof to a mapped list

Totality: total
Visibility: export