lean2/tests/lean/run/induniv.lean

51 lines
1,015 B
Text

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