Theorems · Theorem · real analysis
contDiffWithinAt_id
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {n : WithTop ℕ∞} {s : Set E} {x : E}, ContDiffWithinAt 𝕜 n id s x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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
- ContDiffWithinAtstatement · cited by 283
- contDiff_idproof · cited by 40
- ContDiff.contDiffWithinAtproof · cited by 17
Cited by12
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.fderivWithin_rightproof · cited by 11
- ModelWithCorners.contMDiffproof · cited by 4
- ContMDiff.inlproof · cited by 3
- ContMDiff.inrproof · cited by 3
- ModelWithCorners.contMDiffOn_symmproof · cited by 3
- ContDiffWithinAt.derivWithinproof · cited by 2
- ContDiffWithinAt.fderivWithin_right_applyproof · cited by 1
- ContDiffWithinAt.hasFDerivWithinAt_nhdsproof · cited by 1
- iteratedDerivWithin_powproof · cited by 1
- contDiffWithinAt_piLp_applyproof · cited by 0
- contDiffWithinAt_fun_idproof · cited by 0
- cot_pi_mul_contDiffWithinAtproof · cited by 0