Theorems · Theorem · real analysis
HasDerivAt.congr_simp
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[inst_3 : TopologicalSpace F] [inst_4 : ContinuousSMul 𝕜 F] (f f_1 : 𝕜 → F),
f = f_1 → ∀ (f' f'_1 : F), f' = f'_1 → ∀ (x x_1 : 𝕜), x = x_1 → HasDerivAt f f' x = HasDerivAt f_1 f'_1 x_1- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 82 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousSMulstatement and proof · cited by 1,016
- HasDerivAtstatement and proof · cited by 493
Cited by82
Results whose statement or proof uses this declaration.
- HasDerivAt.div_constproof · cited by 18
- HasDerivAt.comp_ofRealproof · cited by 11
- hasDerivAt_mul_constproof · cited by 10
- HasDerivAt.powproof · cited by 8
- HasDerivAt.real_of_complexproof · cited by 7
- Real.hasDerivAt_tanproof · cited by 6
- ContinuousLinearMap.hasDerivAt_of_bilinearproof · cited by 4
- Real.hasDerivAt_fourierCharproof · cited by 4
- HasDerivAt.fun_finsetProdproof · cited by 4
- HasDerivAt.ofReal_compproof · cited by 3
- Complex.hasDerivAt_Gamma_oneproof · cited by 3
- spectrum.hasDerivAt_resolvent_const_leftproof · cited by 3