diff --git a/src/exercises_sources/friday/manifolds.lean b/src/exercises_sources/friday/manifolds.lean index 881343d..cede741 100644 --- a/src/exercises_sources/friday/manifolds.lean +++ b/src/exercises_sources/friday/manifolds.lean @@ -462,8 +462,7 @@ be a smooth manifold. -/ So, one can prescribe an element of the tangent bundle as a pair (more on this below) -/ example : tangent_bundle 𝓡1 myℝ := ⟨(4 : ℝ), 0⟩ -/- Construct the smooth manifold structure on the tangent bundle. Hint: the answer is a one-liner, -and this instance is not really needed. -/ +/- Type-class inference can construct the smooth manifold structure on the tangent bundle. -/ example : smooth_manifold_with_corners (𝓡1.prod 𝓡1) (tangent_bundle 𝓡1 myℝ) := sorry @@ -475,6 +474,7 @@ equal. And this would be bad. -/ example : charted_space (model_prod ℝ ℝ) (tangent_bundle 𝓡1 myℝ) := sorry + /- The charts of any smooth vector bundle are characterized by `fiber_bundle.charted_space_chart_at` -/ diff --git a/src/solutions/friday/manifolds.lean b/src/solutions/friday/manifolds.lean index 224f2cc..d25f963 100644 --- a/src/solutions/friday/manifolds.lean +++ b/src/solutions/friday/manifolds.lean @@ -515,8 +515,7 @@ be a smooth manifold. -/ So, one can prescribe an element of the tangent bundle as a pair (more on this below) -/ example : tangent_bundle 𝓡1 myℝ := ⟨(4 : ℝ), 0⟩ -/- Construct the smooth manifold structure on the tangent bundle. Hint: the answer is a one-liner, -and this instance is not really needed. -/ +/- Type-class inference can construct the smooth manifold structure on the tangent bundle. -/ example : smooth_manifold_with_corners (𝓡1.prod 𝓡1) (tangent_bundle 𝓡1 myℝ) := -- sorry by apply_instance @@ -532,6 +531,7 @@ example : charted_space (model_prod ℝ ℝ) (tangent_bundle 𝓡1 myℝ) := -- sorry by apply_instance -- sorry + /- The charts of any smooth vector bundle are characterized by `fiber_bundle.charted_space_chart_at` -/