Theorems · Theorem · real analysis
dslope_of_ne
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {a b : 𝕜} (f : 𝕜 → E), b ≠ a → dslope f a b = slope f a b- Defined in
- Mathlib.Analysis.Calculus.DSlope
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 106 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
- derivproof · cited by 676
- Function.update_of_neproof · cited by 198
- slopestatement and proof · cited by 147
- dslopestatement · cited by 40
Cited by7
Results whose statement or proof uses this declaration.
- sub_smul_dslopeproof · cited by 4
- eqOn_dslope_slopeproof · cited by 3
- differentiableWithinAt_dslope_of_neproof · cited by 2
- ContinuousLinearMap.dslope_compproof · cited by 1
- dslope_sub_smul_of_neproof · cited by 1
- Complex.norm_dslope_le_div_of_mapsTo_ballproof · cited by 1