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Mathlib/Geometry/Manifold/VectorBundle/GramSchmidtOrtho.lean

Lines changed: 2 additions & 6 deletions
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@@ -399,24 +399,20 @@ lemma gramSchmidtNormed_continuous (hs : ∀ i, Continuous (T% (s i)))
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end continuity
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#exit
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/-! The Gram-Schmidt process preserves smoothness of sections -/
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section smoothness
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-- Let `V` be a smooth vector bundle with a `C^n` Riemannian structure over a `C^k` manifold `B`.
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variable
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{EB : Type*} [NormedAddCommGroup EB] [NormedSpace ℝ EB]
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{HB : Type*} [TopologicalSpace HB] {IB : ModelWithCorners ℝ EB HB} {n : WithTop ℕ∞}
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{HB : Type*} [TopologicalSpace HB] {IB : ModelWithCorners ℝ EB HB} {k n : WithTop ℕ∞}
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{B : Type*} [TopologicalSpace B] [ChartedSpace HB B]
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{F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F]
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{E : B → Type*} [TopologicalSpace (TotalSpace F E)] [∀ x, NormedAddCommGroup (E x)]
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[∀ x, InnerProductSpace ℝ (E x)] [FiberBundle F E] [VectorBundle ℝ F E]
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[IsManifold IB n B] [ContMDiffVectorBundle n F E IB]
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[IsManifold IB k B] [ContMDiffVectorBundle n F E IB]
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[IsContMDiffRiemannianBundle IB n F E]
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variable {n : WithTop ℕ∞}
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-- TODO: fix pretty-printing of the new differential geometry elaborators!
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set_option linter.style.commandStart false
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