Theorems · Theorem · real analysis
ContDiffWithinAt.rpow_const_of_ne
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E} {s : Set E} {p : ℝ}
{n : WithTop ℕ∞}, ContDiffWithinAt ℝ n f s x → f x ≠ 0 → ContDiffWithinAt ℝ n (fun x => f x ^ p) s x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffWithinAtstatement and proof · cited by 283
- contDiffWithinAt_constproof · cited by 9
- ContDiffWithinAt.rpowproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ContDiffOn.rpow_const_of_neproof · cited by 2