∀ {α : Sort u_1} {r : α → α → Prop} {motive : (a a_1 : α) → Relation.EqvGen r a a_1 → Prop} {a a_1 : α}
  (t : Relation.EqvGen r a a_1),
  (∀ (x y : α) (a : r x y), motive x y ⋯) →
    (∀ (x : α), motive x x ⋯) →
      (∀ (x y : α) (a : Relation.EqvGen r x y), motive x y a → motive y x ⋯) →
        (∀ (x y z : α) (a : Relation.EqvGen r x y) (a_2 : Relation.EqvGen r y z),
            motive x y a → motive y z a_2 → motive x z ⋯) →
          motive a a_1 t