lean2/tests/lean/run/e14.lean

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inductive nat : Type :=
zero : nat,
succ : nat → nat
namespace nat end nat open nat
inductive list (A : Type) : Type :=
nil {} : list A,
cons : A → list A → list A
abbreviation nil := @list.nil
abbreviation cons := @list.cons
check nil
check nil.{1}
check @nil.{1} nat
check @nil nat
check cons nat.zero nil
inductive vector (A : Type) : nat → Type :=
vnil {} : vector A zero,
vcons : forall {n : nat}, A → vector A n → vector A (succ n)
namespace vector end vector open vector
check vcons zero vnil
variable n : nat
check vcons n vnil
check vector.rec
definition vector_to_list {A : Type} {n : nat} (v : vector A n) : list A
:= vector.rec (@nil A) (fun (n : nat) (a : A) (v : vector A n) (l : list A), cons a l) v
coercion vector_to_list
variable f : forall {A : Type}, list A → nat
check f (cons zero nil)
check f (vcons zero vnil)