Theorems · Theorem · global analysis
HasStrictDerivAt.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 → HasStrictDerivAt f f' x = HasStrictDerivAt f_1 f'_1 x_1- Cited by
- 41 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
- HasStrictDerivAtstatement and proof · cited by 163
Cited by41
Results whose statement or proof uses this declaration.
- Complex.hasStrictDerivAt_logproof · cited by 8
- HasStrictDerivAt.real_of_complexproof · cited by 6
- Complex.hasStrictDerivAt_const_cpowproof · cited by 6
- Complex.hasStrictDerivAt_cosproof · cited by 5
- Complex.hasStrictDerivAt_cpow_constproof · cited by 5
- Complex.hasStrictDerivAt_sinproof · cited by 5
- HasStrictFDerivAt.comp_hasStrictDerivAtproof · cited by 5
- hasStrictDerivAt_powproof · cited by 4
- Complex.hasStrictDerivAt_coshproof · cited by 4
- Complex.hasStrictDerivAt_sinhproof · cited by 4
- HasStrictDerivAt.mulproof · cited by 3
- Polynomial.hasStrictDerivAtproof · cited by 3