∀ {α : Type u_1} [inst : UniformSpace α] (_t' : Set (α × α))
  (motive : (∃ t ∈ uniformity α, SetRel.comp t t ⊆ _t') → Prop) (x : ∃ t ∈ uniformity α, SetRel.comp t t ⊆ _t'),
  (∀ (t : Set (α × α)) (ht : t ∈ uniformity α) (htt' : SetRel.comp t t ⊆ _t'), motive ⋯) → motive x