Theorems · Theorem · real analysis
contDiff_zero
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F},
ContDiff 𝕜 0 f ↔ Continuous f- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement · cited by 4,985
- Set.univproof · cited by 3,945
- WithTopstatement · cited by 3,754
- Continuousstatement and proof · cited by 2,592
- ContDiffstatement · cited by 352
- ContDiffOnproof · cited by 294
- continuousOn_univproof · cited by 43
- contDiffOn_univproof · cited by 25
- contDiffOn_zeroproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- ContDiff.continuousproof · cited by 23
- Continuous.fderiv_oneproof · cited by 3
- ContDiffBump.continuousproof · cited by 2
- MeasureTheory.continuous_charFunproof · cited by 1
- Real.contDiffAt_arcsin_iffproof · cited by 1
- expNegInvGlue.contDiff_polynomial_eval_inv_mulproof · cited by 1
- Real.contDiff_rpow_const_of_leproof · cited by 1
- ContDiff.continuous_zeroproof · cited by 0
- Continuous.fderivproof · cited by 0