Theorems · Theorem · real analysis
ContDiffWithinAt.congr_of_eventuallyEq_insert
∀ {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] {s : Set E}
{f f₁ : E → F} {x : E} {n : WithTop ℕ∞},
ContDiffWithinAt 𝕜 n f s x → f₁ =ᶠ[nhdsWithin x (insert x s)] f → ContDiffWithinAt 𝕜 n f₁ s x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- nhdsWithinstatement and proof · cited by 1,912
- Filter.EventuallyEqstatement and proof · cited by 1,912
- ContDiffWithinAtstatement and proof · cited by 283
- Set.mem_insertproof · cited by 109
- Set.subset_insertproof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.fderivWithin''proof · cited by 1
- Filter.EventuallyEq.congr_contDiffWithinAt_of_insertproof · cited by 0