∀ {Y : Type u_1} [inst : TopologicalSpace Y]
  (motive : (PathConnectedSpace Y ∧ ∀ {x y : Y} (p₁ p₂ : Path x y), p₁.Homotopic p₂) → Prop)
  (h : PathConnectedSpace Y ∧ ∀ {x y : Y} (p₁ p₂ : Path x y), p₁.Homotopic p₂),
  (∀ (hpc : PathConnectedSpace Y) (hall : ∀ {x y : Y} (p₁ p₂ : Path x y), p₁.Homotopic p₂), motive ⋯) → motive h