Theorems · Theorem · real analysis
sub_smul_dslope
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] (f : 𝕜 → E) (a b : 𝕜), (b - a) • dslope f a b = f b - f a- Defined in
- Mathlib.Analysis.Calculus.DSlope
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- eq_or_neproof · cited by 1,117
- sub_selfproof · cited by 996
- zero_smulproof · cited by 716
- derivproof · cited by 676
- dslopestatement · cited by 40
- dslope_of_neproof · cited by 7
- dslope_sameproof · cited by 6
- sub_smul_slopeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.of_dslopeproof · cited by 3
- ContinuousWithinAt.of_dslopeproof · cited by 3
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- sub_smul_dslope_of_zeroproof · cited by 1