case intro
X : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : ContractibleSpace X
hv : X ≃ₕ Unit
⊢ Nullhomotopic (ContinuousMap.id X)
X : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : ContractibleSpace X
⊢ Nullhomotopic (ContinuousMap.id X)
obtain ⟨hv⟩ := ContractibleSpace.hequiv_unit X
case intro
X : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : ContractibleSpace X
hv : X ≃ₕ Unit
⊢ Homotopic (ContinuousMap.id X) (const X (↑hv.invFun ()))
case intro
X : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : ContractibleSpace X
hv : X ≃ₕ Unit
⊢ Nullhomotopic (ContinuousMap.id X)
use hv.invFun ()
no goals
case intro
X : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : ContractibleSpace X
hv : X ≃ₕ Unit
⊢ Homotopic (ContinuousMap.id X) (const X (↑hv.invFun ()))
convert hv.left_inv.symm