[Merged by Bors] - feat: add a version of FTC-2 with an integral over the unit interval #8615
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MichaelStollBayreuth
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Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
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…8615) This adds the following version of the Fundamental Theorem of Calculus: ```lean lemma integral_unitInterval_eq_sub {C E : Type*} [IsROrC C] [NormedAddCommGroup E] [NormedSpace ℝ E] [NormedSpace C E] [CompleteSpace E] [IsScalarTower ℝ C E] {f f' : C → E} {z₀ z₁ : C} (hcont : ContinuousOn (fun t : ℝ ↦ f' (z₀ + t • z₁)) (Set.Icc 0 1)) (hderiv : ∀ t ∈ Set.Icc (0 : ℝ) 1, HasDerivAt f (f' (z₀ + t • z₁)) (z₀ + t • z₁)) : z₁ • ∫ t in (0 : ℝ)..1, f' (z₀ + t • z₁) = f (z₀ + z₁) - f z₀ := ... ``` This is helpful for, e.g., estimating the complex logarithm. Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
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…8615) This adds the following version of the Fundamental Theorem of Calculus: ```lean lemma integral_unitInterval_eq_sub {C E : Type*} [IsROrC C] [NormedAddCommGroup E] [NormedSpace ℝ E] [NormedSpace C E] [CompleteSpace E] [IsScalarTower ℝ C E] {f f' : C → E} {z₀ z₁ : C} (hcont : ContinuousOn (fun t : ℝ ↦ f' (z₀ + t • z₁)) (Set.Icc 0 1)) (hderiv : ∀ t ∈ Set.Icc (0 : ℝ) 1, HasDerivAt f (f' (z₀ + t • z₁)) (z₀ + t • z₁)) : z₁ • ∫ t in (0 : ℝ)..1, f' (z₀ + t • z₁) = f (z₀ + z₁) - f z₀ := ... ``` This is helpful for, e.g., estimating the complex logarithm. Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
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This adds the following version of the Fundamental Theorem of Calculus:
This is helpful for, e.g., estimating the complex logarithm.