Theorems · Theorem · real analysis
ContDiffAt.div
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : E} {f g : E → 𝕜} {n : WithTop ℕ∞},
ContDiffAt 𝕜 n f x → ContDiffAt 𝕜 n g x → g x ≠ 0 → ContDiffAt 𝕜 n (f / g) x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 262
- ContDiffWithinAt.divproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ContDiff.divproof · cited by 2
- Complex.contDiffAt_tanproof · cited by 1
- ContDiffAt.fun_divproof · cited by 0