Definition relation (A : Type) := A -> A -> Type.
Class Reflexive {A} (R : relation A) := reflexivity : forall x : A, R x x.
Existing Class IsHProp.
Inductive Empty : Set := .
Notation "~ x" := (x -> Empty) : type_scope.
Record hProp := BuildhProp { type :> Type ; trunc : IsHProp type }.
Arguments BuildhProp _ {_}.
Canonical Structure default_hProp := fun T P => (@BuildhProp T P).
Generalizable Variables A B f g e n.
Existing Instance trunc_forall.
Inductive V : Type := | set {A : Type} (f : A -> V) : V.

Axiom mem : V -> V -> hProp.
Axiom mem_induction
: forall (C : V -> hProp), (forall v, (forall x, mem x v -> C x) -> C v) -> forall v, C v.