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iteratedFDerivWithin_zero_apply, Function.comp_apply, LinearIsometryEquiv.comp_fderivWithin _ (hs x hx)] simp | succ n IH => let I := (continuousMultilinearCurryRightEquiv' π•œ n E F).symm have A : βˆ€ y ∈ s, iteratedFDerivWithin π•œ n.succ f s y = (I ∘ iteratedFDerivWithin π•œ n (fun y => fderiv...
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lemma iteratedFDeriv_comp_add_right' (n : β„•) (a : E) : iteratedFDeriv π•œ n (fun z ↦ f (z + a)) = fun x ↦ iteratedFDeriv π•œ n f (x + a) := by simpa [add_comm a] using iteratedFDeriv_comp_add_left' n a /-- The iterated derivative commutes with shifting the function by a constant on the right. -/ lemma iteratedFDer...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Defs public import Mathlib.Analysis.Calculus.MeanValue /-! # Higher differentiabilit...
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/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Comp public import Mathlib.Analysis.Calculus.ParametricIntegral public import Mathlib.Analysis.Convolutio...
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/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ module public import Mathlib.Analysis.Calculus.ContDiff.Defs public import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars /-! ### Restricting Scalars in Iterated ...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Basic public import Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno public import Mathl...
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@[fun_prop] theorem ContDiff.smulRight {f : E β†’ StrongDual π•œ F} {g : E β†’ G} (hf : ContDiff π•œ n f) (hg : ContDiff π•œ n g) : ContDiff π•œ n fun x => (f x).smulRight (g x) := isBoundedBilinearMap_smulRight.contDiff.compβ‚‚ (g := fun p => p.1.smulRight p.2) hf hg @[fun_prop] theorem ContDiffOn.smulRight {f : E β†’ Stro...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Comp /-! # Higher differentiability in one dimension The general theory of higher d...
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/- Copyright (c) 2024 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Data.Finite.Card public import Mathlib.Analysis.Analytic.Within public import Mathlib.Analysis.Calculus.FDeriv.Analytic public imp...
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refine ⟨pred (Fin.cast A i) (by simpa using i_ne), Fin.cast (by simp) j, ?_⟩ have : x = pred (succ x) (succ_ne_zero x) := rfl rw [this] congr rw [← hij] congr 1 Β· simp Β· simp [Fin.heq_ext_iff] /-- Given an ordered finpartition of `n+1`, with a leftmost atom different from `{0}`, remove `{0}...
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Matrix.zero_empty, ContinuousLinearMap.flipMultilinear_apply_apply, compAlongOrderedFinpartitionL_apply, compAlongOrderFinpartition_apply] congr ext j exact Fin.cases rfl (fun i ↦ rfl) j /-- Composing a formal multilinear series with an ordered partition extended by adding a left point to an already existing...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Defs public import Mathlib.Analysis.Calculus.FDeriv.Affine /-! # Basic properties of...
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/-- Composition by continuous linear equivs on the right respects higher differentiability on domains. -/ theorem ContinuousLinearEquiv.contDiffOn_comp_iff (e : G ≃L[π•œ] E) : ContDiffOn π•œ n (f ∘ e) (e ⁻¹' s) ↔ ContDiffOn π•œ n f s := ⟨fun H => by simpa [Function.comp_def] using H.comp_continuousLinearMap (e.symm ...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Analysis.Normed.Module.FiniteDimension /-! # Higher...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Comp public import Mathlib.Analysis.Calculus.Deriv.Inverse public import Mathlib.Topo...
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theorem ContDiffOn.smul {s : Set E} {f : E β†’ π•œ'} {g : E β†’ F} (hf : ContDiffOn π•œ n f s) (hg : ContDiffOn π•œ n g s) : ContDiffOn π•œ n (f β€’ g) s := fun x hx => (hf x hx).smul (hg x hx) end SMul /-! ### Constant scalar multiplication TODO: generalize results in this section -- if `c` is a unit (or `R` is a group...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Analytic.Within public import Mathlib.Analysis.Calculus.FDeriv.Analytic public import Mathlib.Analysis.Calculus.ContDiff....
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refine ⟨insert x s ∩ u, ?_, p, hp.mono hut, fun i ↦ (h'p i).mono hut⟩ simp only [insert_eq_of_mem, hy, self_mem_nhdsWithin] Β· match m with | Ο‰ => simp [hn] at hm | ∞ => exact (hn (h' rfl)).elim | (m : β„•) => rcases contDiffWithinAt_nat.1 (h.of_le hm) with ⟨t, ht, p, hp⟩ rcases mem_nhdsWithi...
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theorem ContDiffAt.differentiableAt (h : ContDiffAt π•œ n f x) (hn : n β‰  0) : DifferentiableAt π•œ f x := by simpa [hn, differentiableWithinAt_univ] using h.differentiableWithinAt theorem ContDiffAt.differentiableAt_iteratedFDeriv {f : E β†’ F} {n : β„•βˆžΟ‰} {m : β„•} {x : E} (h : ContDiffAt π•œ n f x) (hmn : ↑m < n) :...
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/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ module public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Analysis.Normed.Lp.PiLp /-! # Derivatives on `WithLp` -/ ...
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/- Copyright (c) 2025 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ module public import Mathlib.Algebra.Polynomial.AlgebraMap public import Mathlib.Analysis.Calculus.ContDiff.Operations /-! # Higher smoothness of polynomials We ...
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/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.FDeriv.Analytic public import Mathlib.Analysis.Calculus.ContDiff.Defs /-! # Higher smoothness of continuously polyn...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Data.Finset.Sym public import Mathlib.Data.Nat.Choos...
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_ = βˆ‘ i ∈ Finset.range (n + 1), (n ! : ℝ) * ((i ! : ℝ)⁻¹ * i !) * C * (D ^ i * D ^ (n - i + 1)) * ((n - i)! : ℝ)⁻¹ := by congr! 1 with i hi simp only [Nat.cast_choose ℝ (Finset.mem_range_succ_iff.1 hi), div_eq_inv_mul, mul_inv] ring _ = βˆ‘ i ∈ Finset.range (n + 1), (n ! : ℝ) * 1 * C * D ^ (...
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/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang -/ module public import Mathlib.Analysis.Calculus.Conformal.NormedSpace public import Mathlib.Analysis.InnerProductSpace.ConformalLinearMap /-! # Conformal maps between in...
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/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang -/ module public import Mathlib.Analysis.Calculus.FDeriv.Add public import Mathlib.Analysis.Calculus.FDeriv.Const public import Mathlib.Analysis.Normed.Operator.Conformal ...
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/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.LineDeriv.Basic public import Mathlib.Analysis.Calculus.Deriv.Mul public import Mathlib.LinearAlgebra.QuadraticForm....
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/- Copyright (c) 2024 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.LineDeriv.Basic public import Mathlib.MeasureTheory.Integral.IntegralEqImproper /-! # Integration by parts for ...
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/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.Deriv.Comp public import Mathlib.Analysis.Calculus.Deriv.Add public import Mathlib.Analysis.Calculus.Deriv.Mul p...
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⟨fun h ↦ by simpa [smul_smul, inv_mul_cancelβ‚€ hc] using h.smul (c ⁻¹), fun h ↦ h.smul c⟩ theorem LineDifferentiableWithinAt.smul (h : LineDifferentiableWithinAt π•œ f s x v) (c : π•œ) : LineDifferentiableWithinAt π•œ f s x (c β€’ v) := (h.hasLineDerivWithinAt.smul c).lineDifferentiableWithinAt theorem lineDifferenti...
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/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.LineDeriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Measurable /-! # Measurability of the line deriv...
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/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.BumpFunction.Basic public import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap public import Mathlib....
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/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ module public import Mathlib.Analysis.Convolution public import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension public import Mathlib.Analysis.Calculus.Bu...
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/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Analysis.Normed.Module.FiniteDimension /-! # Infinit...
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/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.SmoothSeries public import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct public import Mathlib.Analysis.Ca...
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/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.BumpFunction.Basic public import Mathlib.Analysis.InnerProductSpace.Calculus public import Math...
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/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.BumpFunction.Convolution public import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension /-! # Density of smoo...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.FDeriv.Pow /-! # Derivative of `(f x) ^ n`, `n : β„•` In this file we prove that the FrΓ©chet derivative of `fun ...
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/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Comp public import Mathlib.Analysis.Calculus.FDeriv.Equiv /-! # Inverse function theorem - the easy half In ...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, SΓ©bastien GouΓ«zel, Yury Kudryashov, Yuyang Zhao -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Comp public ...
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/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic /-! # Support of the derivative of a function In this file we prove that the (topological) support o...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, SΓ©bastien GouΓ«zel, Yury Kudryashov, Anatole Dedecker -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Add /-...
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/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Star /-! # Star operations on derivatives This file contains th...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Yury Kudryashov, Eric Wieser -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Prod /-! # Derivatives of func...
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/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Add public import Mathlib.Analysis.Calculus.Deriv.Linear public import Mathlib.LinearAlgebra.AffineSpace.Affin...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic public import Mathlib.Analysis.Calculus.FDeriv.Linear /-! # Derivatives of continuous line...
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/- Copyright (c) 2023 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ module public import Mathlib.Analysis.Calculus.FDeriv.Pi public import Mathlib.Analysis.Calculus.Deriv.Basic /-! # One-dimensional derivatives ...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Anatole Dedecker, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Support public import Mathlib.Analysis.Calculus.FDeriv.Mul public import Mathli...
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simpa [add_comm] using (hc.hasFDerivWithinAt.clm_comp hd.hasFDerivWithinAt).hasDerivWithinAt theorem HasDerivAt.clm_comp (hc : HasDerivAt c c' x) (hd : HasDerivAt d d' x) : HasDerivAt (fun y => (c y).comp (d y)) (c'.comp (d x) + (c x).comp d') x := by rw [← hasDerivWithinAt_univ] at * exact hc.clm_comp hd the...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.FDeriv.Const public import Mathlib.Analysis.Calculus.TangentCone.DimOne public import Mathlib.Analysi...
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theorem HasDerivWithinAt.congr_of_eventuallyEq_of_mem (h : HasDerivWithinAt f f' s x) (h₁ : f₁ =αΆ [𝓝[s] x] f) (hx : x ∈ s) : HasDerivWithinAt f₁ f' s x := h.congr_of_eventuallyEq h₁ (h₁.eq_of_nhdsWithin hx) theorem Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem (h₁ : f₁ =αΆ [𝓝[s] x] f) (hx : x ∈ s) : HasDeri...
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/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Add public import Mathlib.LinearAlgebra.AffineSpace.Slope public import Mathlib.Topology.Algebra.Module.Perfec...
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/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Pow public import Mathlib.Analysis.Calculus.Deriv.Inv public import Mathlib.Analysis.Calc...
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/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.FDeriv.Equiv public import Mathlib.Analysis.Calculus.Deriv.Mul /-! # Derivative of `x ↦ f (cx)` In this file we pr...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Eric Wieser -/ module public import Mathlib.Algebra.Polynomial.AlgebraMap public import Mathlib.Algebra.Polynomial.Derivative public import Mathlib.Analysis.Calc...
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/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Calculus.Deriv.Add public import Mathlib.Analysis.Calculus.Deriv.Comp public import Mathlib.Analysis.Calculus.Deriv...
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/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.Deriv.AffineMap public import Mathlib.Analysis.Calculus.Deriv.Comp public import Mathlib.Analysis...
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`f` is a strictly antitone function. Note that we don't require differentiability explicitly as it already implied by the derivative being strictly negative. -/ theorem strictAnti_of_deriv_neg {f : ℝ β†’ ℝ} (hf' : βˆ€ x, deriv f x < 0) : StrictAnti f := strictAntiOn_univ.1 <| strictAntiOn_of_deriv_neg convex_univ (...
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/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ module public import Mathlib.Analysis.Calculus.Deriv.Add public import Mathlib.Analysis.InnerProductSpace.Calculus /-! # Derivative of the absolute value This file...
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/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Mul public import Mathlib.Analysis.Calculus.Deriv.Comp /-! # Derivatives of `x ↦ x⁻¹` an...
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/- Copyright (c) 2025 A Tucker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: A Tucker -/ module public import Mathlib.Analysis.Calculus.Implicit /-! # Implicit function theorem β€” domain a product space This specialization of the implicit function theorem applies t...
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/- Copyright (c) 2026 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.ContDiff.Comp public import Mathlib.Topology.MetricSpace.Holder /-! # Continuously `k` times differentiable functio...
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/- Copyright (c) 2025 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ module public import Mathlib.Analysis.Analytic.Inverse public import Mathlib.Analysis.Calculus.FDeriv.Analytic public import Mathlib.Analysis.Calculus.InverseFunctio...
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/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Inverse public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv /-! # Inverse function theorem,...
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/- Copyright (c) 2020 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ module public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Analysis.Calculus.ContDiff.RCLike public import Mathlib.Analysis.Calculus....
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/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Normed.Operator.Banach public import Mathlib.Analysis.Normed.Operator.NormedSpace public import Mathlib.To...
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/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.FDeriv.Equiv public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn ...
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/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn public import Mathlib.Analysis.Normed.Module.FiniteDimension /-! # ...
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/- Copyright (c) 2025 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Seminorm public import Mathlib.Analysis.Calculus.TangentCone.Defs /-! # Tangent cone in a proper space In this file we ...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.TangentCone.Basic public import Mathlib.Topology.Algebra.MulAction public import Mathlib.Analys...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.TangentCone.Defs public import Mathlib.LinearAlgebra.Prod public import Mathlib.Topology.Algebr...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.TangentCone.Basic import Mathlib.Topology.Algebra.Module.Basic /-! # Indexed product of sets with unique differ...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.TangentCone.Defs public import Mathlib.Topology.Algebra.Group.Basic public import Mathlib.LinearAlgebra.Span.Bas...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Order.Filter.Pointwise public import Mathlib.Analysis.Normed.Group.Basic public import Mathlib.LinearAlgebra.Span.Defs /-! # Tang...
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/- Copyright (c) 2025 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.TangentCone.Defs import Mathlib.Analysis.Calculus.TangentCone.Basic import Mathlib.Analysis.Nor...
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/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.TangentCone.Basic public import Mathlib.Analysis.Convex.Topology public import Mathlib.Analysis.Normed.Field.Bas...
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/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.LocalExtr.Basic public import Mathlib.Analysis.Calculus.LineDeriv.Basic /-! # Local extremum and line derivatives ...
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/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Add /-! # Local extrema of differentiable functions ## Main definitions In a real normed space `E` we defin...
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/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.LocalExtr.Rolle public import Mathlib.Analysis.Calculus.Deriv.Polynomial public import Mathlib....
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/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Anatole Dedecker -/ module public import Mathlib.Analysis.Calculus.LocalExtr.Basic public import Mathlib.Topology.Order.Rolle /-! # Rolle's Theorem In this file we...
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/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, YaΓ«l Dillies -/ module -- shake: keep-all public import Mathlib.Analysis.Normed.Group.Basic /-! # Ordered normed spaces In this file, we define classes for field...
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/- Copyright (c) 2022 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ module public import Mathlib.Algebra.Order.Field.Pi public import Mathlib.Algebra.Order.Pi public import Mathlib.Analysis.Normed.Field.Basic public import Mathlib.Analys...
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/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ module public import Mathlib.Analysis.Normed.Group.Constructions public import Mathlib.Analysis.Normed.Group.Rat public import Mathlib.Analysis.Normed.Group....
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/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ module public import Mathlib.Analysis.Normed.Group.Hom public import Mathlib.Analysis.Normed.Group.Completion /-! # Completion of normed group homs Given two (semi...
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/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes HΓΆlzl, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Group.Real public import Mathlib.Topology.Instances.Int /-! # β„€ as a normed group -/ @[e...
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/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes HΓΆlzl, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Group.Continuity public import Mathlib.Topology.Algebra.IsUniformGroup.Basic public import...
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/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ module public import Mathlib.Algebra.Order.Group.Indicator public import Mathlib.Analysis.Normed.Group.Basic /-! # Indicator function and (e)norm Th...
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/- Copyright (c) 2022 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ module public import Mathlib.Analysis.Normed.Group.Uniform /-! # Further lemmas about normed groups This file contains further lemmas about normed groups, requirin...
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/- Copyright (c) 2021 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Heather Macbeth, Johannes HΓΆlzl, Yury Kudryashov -/ module public import Mathlib.Algebra.BigOperators.Intervals public import Mathlib.Analysis.Normed.Group.Real ...
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/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ module public import Mathlib.Analysis.Normed.Group.Quotient public import Mathlib.Analysis.Normed.Module.Ball.Pointwise public import Mathlib.Topology.Instances.AddCircle....
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/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes HΓΆlzl, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Group.Int public import Mathlib.Topology.Instances.Rat /-! # β„š as a normed group -/ @[ex...
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/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky, David Loeffler -/ module public import Mathlib.Analysis.Normed.Group.Uniform public import Mathlib.Topology.Algebra.Nonarchimedean.Basic public import Mathlib.Topolo...
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/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yury Kudryashov -/ module public import Mathlib.Analysis.Normed.Group.Constructions public import Mathlib.Analysis.Normed.Group.Submodule public import Mathlib.LinearAlgeb...
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/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ module public import Mathlib.Analysis.RCLike.Basic public import Mathlib.Analysis.Normed.Group.InfiniteSum /-! # Tannery's theorem Tannery's theorem gives a suffic...
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/- Copyright (c) 2021 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Group.Bounded public import Mathlib.Analysis.Normed.Group.Uniform public import Mathlib.Topology.Met...
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/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ module public import Mathlib.Analysis.Normed.Group.Uniform public import Mathlib.Topology.Algebra.GroupCompletion public import Mathlib.Topology.MetricSpace.Completi...
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/- Copyright (c) 2024 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ module public import Mathlib.Analysis.Normed.Group.Basic public import Mathlib.Topology.ContinuousMap.CocompactMap public import Mathlib.Topology.MetricSpace.Bounded /-! ...
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/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ module public import Mathlib.Analysis.Normed.Group.Hom public import Mathlib.Topology.Algebra.SeparationQuotient.Hom /-! # Lifts of maps to separation quotients of semi...
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/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ module public import Mathlib.Analysis.Normed.Group.Continuity public import Mathlib.Analysis.Normed.MulAction /-! # The null subgroup in a seminormed commutative group ...
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/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes HΓΆlzl, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Group.Defs public import Mathlib.Data.NNReal.Basic public import Mathlib.Topology.Algebra....