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fix/docs: fix typo in example code (#14801)
`EuclideanSpace` requires the field π•œ to be provided explicitly.
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β€ŽMathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean

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@@ -48,25 +48,26 @@ but add these assumptions later as needed. (Quite a few results still do not req
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`extChartAt I x` is the canonical such partial equiv around `x`.
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As specific examples of models with corners, we define (in `Geometry.Manifold.Instances.Real`)
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* `modelWithCornersSelf ℝ (EuclideanSpace (Fin n))` for the model space used to define
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* `modelWithCornersSelf ℝ (EuclideanSpace ℝ (Fin n))` for the model space used to define
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`n`-dimensional real manifolds without boundary (with notation `𝓑 n` in the locale `Manifold`)
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* `ModelWithCorners ℝ (EuclideanSpace (Fin n)) (EuclideanHalfSpace n)` for the model space
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* `ModelWithCorners ℝ (EuclideanSpace ℝ (Fin n)) (EuclideanHalfSpace n)` for the model space
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used to define `n`-dimensional real manifolds with boundary (with notation `π“‘βˆ‚ n` in the locale
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`Manifold`)
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* `ModelWithCorners ℝ (EuclideanSpace (Fin n)) (EuclideanQuadrant n)` for the model space used
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* `ModelWithCorners ℝ (EuclideanSpace ℝ (Fin n)) (EuclideanQuadrant n)` for the model space used
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to define `n`-dimensional real manifolds with corners
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With these definitions at hand, to invoke an `n`-dimensional real manifold without boundary,
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one could use
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`variable {n : β„•} {M : Type*} [TopologicalSpace M] [ChartedSpace (EuclideanSpace (Fin n)) M]
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`variable {n : β„•} {M : Type*} [TopologicalSpace M] [ChartedSpace (EuclideanSpace ℝ (Fin n)) M]
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[SmoothManifoldWithCorners (𝓑 n) M]`.
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However, this is not the recommended way: a theorem proved using this assumption would not apply
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for instance to the tangent space of such a manifold, which is modelled on
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`(EuclideanSpace (Fin n)) Γ— (EuclideanSpace (Fin n))` and not on `EuclideanSpace (Fin (2 * n))`!
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`(EuclideanSpace ℝ (Fin n)) Γ— (EuclideanSpace ℝ (Fin n))`
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and not on `EuclideanSpace ℝ (Fin (2 * n))`!
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In the same way, it would not apply to product manifolds, modelled on
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`(EuclideanSpace (Fin n)) Γ— (EuclideanSpace (Fin m))`.
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`(EuclideanSpace ℝ (Fin n)) Γ— (EuclideanSpace ℝ (Fin m))`.
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The right invocation does not focus on one specific construction, but on all constructions sharing
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the right properties, like
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