ruc-ai4math/mathlib_handler_benchmark_410 huggingface dataset:
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>s : Set M<VAR>t : Set M'<VAR>g : M' → M''<VAR>hg : SmoothOn I' I'' g t<VAR>hf : SmoothOn I I' f s<GOAL>SmoothOn I I'' (g ∘ f) (s ∩ f ⁻¹' t)
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>n : ℕ∞<VAR>g : M' → M''<VAR>hg : ContMDiff I' I'' n g<VAR>hf : ContMDiff I I' n f<GOAL>ContMDiff I I'' n (g ∘ f)
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>g : M' → M''<VAR>hg : Smooth I' I'' g<VAR>hf : Smooth I I' f<GOAL>Smooth I I'' (g ∘ f)
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>s : Set M<VAR>n : ℕ∞<VAR>t : Set M'<VAR>g : M' → M''<VAR>x : M<VAR>hg : ContMDiffWithinAt I' I'' n g t (f x)<VAR>hf : ContMDiffWithinAt I I' n f s x<GOAL>ContMDiffWithinAt I I'' n (g ∘ f) (s ∩ f ⁻¹' t) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>s : Set M<VAR>t : Set M'<VAR>g : M' → M''<VAR>x : M<VAR>hg : SmoothWithinAt I' I'' g t (f x)<VAR>hf : SmoothWithinAt I I' f s x<GOAL>SmoothWithinAt I I'' (g ∘ f) (s ∩ f ⁻¹' t) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>s : Set M<VAR>n : ℕ∞<VAR>g : M' → M''<VAR>x : M<VAR>hg : ContMDiffAt I' I'' n g (f x)<VAR>hf : ContMDiffWithinAt I I' n f s x<GOAL>ContMDiffWithinAt I I'' n (g ∘ f) s x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>s : Set M<VAR>g : M' → M''<VAR>x : M<VAR>hg : SmoothAt I' I'' g (f x)<VAR>hf : SmoothWithinAt I I' f s x<GOAL>SmoothWithinAt I I'' (g ∘ f) s x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>n : ℕ∞<VAR>g : M' → M''<VAR>x : M<VAR>hg : ContMDiffAt I' I'' n g (f x)<VAR>hf : ContMDiffAt I I' n f x<GOAL>ContMDiffAt I I'' n (g ∘ f) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>n : ℕ∞<VAR>g : M' → M''<VAR>x : M<VAR>y : M'<VAR>hg : ContMDiffAt I' I'' n g y<VAR>hf : ContMDiffAt I I' n f x<VAR>hx : f x = y<GOAL>ContMDiffAt I I'' n (g ∘ f) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>g : M' → M''<VAR>x : M<VAR>hg : SmoothAt I' I'' g (f x)<VAR>hf : SmoothAt I I' f x<GOAL>SmoothAt I I'' (g ∘ f) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>n : ℕ∞<VAR>f : M → M'<VAR>g : M' → M''<VAR>s : Set M<VAR>hg : ContMDiff I' I'' n g<VAR>hf : ContMDiffOn I I' n f s<GOAL>ContMDiffOn I I'' n (g ∘ f) s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>g : M' → M''<VAR>s : Set M<VAR>hg : Smooth I' I'' g<VAR>hf : SmoothOn I I' f s<GOAL>SmoothOn I I'' (g ∘ f) s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>n : ℕ∞<VAR>t : Set M'<VAR>g : M' → M''<VAR>hg : ContMDiffOn I' I'' n g t<VAR>hf : ContMDiff I I' n f<VAR>ht : ∀ (x : M), f x ∈ t<GOAL>ContMDiff I I'' n (g ∘ f)
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>E'' : Type u_8<VAR>NormedAddCommGroup E''<VAR>NormedSpace 𝕜 E''<VAR>H'' : Type u_9<VAR>TopologicalSpace H''<VAR>I'' : ModelWithCorners 𝕜 E'' H''<VAR>M'' : Type u_10<VAR>TopologicalSpace M''<VAR>ChartedSpace H'' M''<VAR>f : M → M'<VAR>t : Set M'<VAR>g : M' → M''<VAR>hg : SmoothOn I' I'' g t<VAR>hf : Smooth I I' f<VAR>ht : ∀ (x : M), f x ∈ t<GOAL>Smooth I I'' (g ∘ f)
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>n : ℕ∞<GOAL>ContMDiff I I n id
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<GOAL>Smooth I I id
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>s : Set M<VAR>n : ℕ∞<GOAL>ContMDiffOn I I n id s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>s : Set M<GOAL>SmoothOn I I id s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>x : M<VAR>n : ℕ∞<GOAL>ContMDiffAt I I n id x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>x : M<GOAL>SmoothAt I I id x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>s : Set M<VAR>x : M<VAR>n : ℕ∞<GOAL>ContMDiffWithinAt I I n id s x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>s : Set M<VAR>x : M<GOAL>SmoothWithinAt I I id s x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>n : ℕ∞<VAR>c : M'<GOAL>ContMDiff I I' n fun x => c
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>n : ℕ∞<VAR>Zero M'<GOAL>ContMDiff I I' n 0
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>n : ℕ∞<VAR>One M'<GOAL>ContMDiff I I' n 1
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>c : M'<GOAL>Smooth I I' fun x => c
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>One M'<GOAL>Smooth I I' 1
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>Zero M'<GOAL>Smooth I I' 0
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>n : ℕ∞<VAR>c : M'<GOAL>ContMDiffOn I I' n (fun x => c) s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>n : ℕ∞<VAR>One M'<GOAL>ContMDiffOn I I' n 1 s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>n : ℕ∞<VAR>Zero M'<GOAL>ContMDiffOn I I' n 0 s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>c : M'<GOAL>SmoothOn I I' (fun x => c) s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>Zero M'<GOAL>SmoothOn I I' 0 s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>One M'<GOAL>SmoothOn I I' 1 s
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>n : ℕ∞<VAR>c : M'<GOAL>ContMDiffAt I I' n (fun x => c) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>n : ℕ∞<VAR>Zero M'<GOAL>ContMDiffAt I I' n 0 x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>n : ℕ∞<VAR>One M'<GOAL>ContMDiffAt I I' n 1 x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>c : M'<GOAL>SmoothAt I I' (fun x => c) x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>Zero M'<GOAL>SmoothAt I I' 0 x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>x : M<VAR>One M'<GOAL>SmoothAt I I' 1 x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>x : M<VAR>n : ℕ∞<VAR>c : M'<GOAL>ContMDiffWithinAt I I' n (fun x => c) s x
<VAR>𝕜 : Type u_1<VAR>NontriviallyNormedField 𝕜<VAR>E : Type u_2<VAR>NormedAddCommGroup E<VAR>NormedSpace 𝕜 E<VAR>H : Type u_3<VAR>TopologicalSpace H<VAR>I : ModelWithCorners 𝕜 E H<VAR>M : Type u_4<VAR>TopologicalSpace M<VAR>ChartedSpace H M<VAR>E' : Type u_5<VAR>NormedAddCommGroup E'<VAR>NormedSpace 𝕜 E'<VAR>H' : Type u_6<VAR>TopologicalSpace H'<VAR>I' : ModelWithCorners 𝕜 E' H'<VAR>M' : Type u_7<VAR>TopologicalSpace M'<VAR>ChartedSpace H' M'<VAR>s : Set M<VAR>x : M<VAR>n : ℕ∞<VAR>Zero M'<GOAL>ContMDiffWithinAt I I' n 0 s x