Universe Set_u.
Universe Set_V.
Constraint Set_u < Set_V.
Create HintDb aczel_hints.
Inductive Tree : Type@{Set_V} :=
| mkNode (cs : Type@{Set_u}) (ts : forall c : cs, Tree) : Tree.
Fixpoint eqTree (lhs : Tree) (rhs : Tree) : Prop :=
match lhs, rhs with
| mkNode cs1 ts1, mkNode cs2 ts2 => (forall c1 : cs1, exists c2 : cs2, eqTree (ts1 c1) (ts2 c2)) /\ (forall c2 : cs2, exists c1 : cs1, eqTree (ts1 c1) (ts2 c2))
end.
#[global]
Instance eqTree_Reflexive
: Reflexive eqTree.
#[global] Hint Resolve member_intro : aczel_hints.
Definition isSubsetOf x y : Prop :=
forall z, z \in x -> z \in y.
#[local] Infix "\subseteq" := isSubsetOf : type_scope.
#[global] Hint Unfold isSubsetOf : aczel_hints.
#[global]
Instance isSubsetOf_PreOrder
: PreOrder isSubsetOf.
#[global]
Instance isSubsetOf_PartialOrder
: PartialOrder eqProp isSubsetOf.

Lemma eqTree_intro (lhs : Tree) (rhs : Tree)
(SUBSET : lhs \subseteq rhs)
(SUBSET' : rhs \subseteq lhs)
: lhs == rhs.