[Merged by Bors] - feat(geometry/manifold): lemmas from the sphere eversion project #18877
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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) * Also adds a new library note `comp_of_eq lemmas` about how (I think) we should better formulate composition lemmas of properties of functions. * About the library note `comp_of_eq lemmas`: exactly the same problems happen in Lean 4. * renamings ``` smooth_iff_proj_smooth -> smooth_prod_iff differentiable_at.fderiv_within_prod -> differentiable_within_at.fderiv_within_prod ``` * We add a `path_connected_space` instance of the tangent space. This instance is sufficient to compile sphere-eversion, without any `normed_space` instances on the tangent space (which are not the canonical structure on the tangent space). * From the sphere eversion project
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Forward-port of leanprover-community/mathlib#18877 (2 files)
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Forward-port of leanprover-community/mathlib#18877 (2 files)
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comp_of_eq lemmasabout how (I think) we should better formulate composition lemmas of properties of functions.comp_of_eq lemmas: exactly the same problems happen in Lean 4.path_connected_spaceinstance of the tangent space. This instance is sufficient to compile sphere-eversion, without anynormed_spaceinstances on the tangent space (which are not the canonical structure on the tangent space).