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Theorems · Theorem · real analysis

dslope_sub_smul_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 (fun x => (x - a) • f x) a b = f b
Defined in
Mathlib.Analysis.Calculus.DSlope
Cited by
1 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

eqOn_dslope_sub_smul · cited by 1eqOn_dslope_sub_smulNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFielddslope · cited by 40dslopedslope_of_ne · cited by 7dslope_of_neslope_sub_smul · cited by 1slope_sub_smuldslope_sub_smul_of_neCITED BYCITES

Cites6

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Cited by1

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