Theorems · Theorem · real analysis
contDiffAt_const
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {x : E} {n : WithTop ℕ∞}
{c : F}, ContDiffAt 𝕜 n (fun x => c) x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffAtstatement · cited by 262
- ContDiff.contDiffAtproof · cited by 106
- contDiff_constproof · cited by 36
Cited by15
Results whose statement or proof uses this declaration.
- contDiffWithinAt_constproof · cited by 9
- Real.contDiffAt_rpow_of_neproof · cited by 4
- contMDiffAt_localFrameCoeffproof · cited by 3
- Real.deriv_sqrt_auxproof · cited by 2
- Real.deriv_arcsin_auxproof · cited by 2
- ContDiffAt.contDiffAt_implicitFunctionproof · cited by 1
- Real.contDiffAt_rpow_const_of_neproof · cited by 1
- OpenPartialHomeomorph.contDiffOn_univUnitBall_symmproof · cited by 1
- ContDiffAt.contDiffAt_norm_of_smulproof · cited by 0
- Real.contDiffAt_arccosproof · cited by 0
- Real.contDiffAt_arccos_iffproof · cited by 0
- InnerProductSpace.harmonicAt_constproof · cited by 0