prelude
inductive list (A : Type) : Type :=
nil {} : list A,
cons   : A → list A → list A

section
  variable A : Type
  inductive list2 : Type :=
  nil2 {} : list2,
  cons2   : A → list2 → list2
end

constant num : Type.{1}

namespace Tree
inductive tree (A : Type) : Type :=
node : A → forest A → tree A
with forest : Type :=
nil  : forest A,
cons : tree A → forest A → forest A
end Tree

inductive group_struct (A : Type) : Type :=
mk_group_struct : (A → A → A) → A → group_struct A

inductive group : Type :=
mk_group : Π (A : Type), (A → A → A) → A → group

section
  variable A : Type
  variable B : Type
  inductive pair : Type :=
  mk_pair : A → B → pair
end

definition Prop := Type.{0}
inductive eq {A : Type} (a : A) : A → Prop :=
refl : eq a a

section
  variable {A : Type}
  inductive eq2 (a : A) : A → Prop :=
  refl2 : eq2 a a
end


section
  variable A : Type
  variable B : Type
  inductive triple (C : Type) : Type :=
  mk_triple : A → B → C → triple C
end
