Theorems · Theorem · global analysis
tangentConeAt_mono
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : SMul 𝕜 E] [inst_2 : TopologicalSpace E] {s t : Set E}
{x : E}, s ⊆ t → tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Set.preimageproof · cited by 4,946
- nhdsWithinproof · cited by 1,912
- ClusterPtproof · cited by 138
- Set.preimage_monoproof · cited by 95
- nhdsWithin_monoproof · cited by 82
- tangentConeAtstatement · cited by 54
- ClusterPt.monoproof · cited by 30
- tangentConeAt_defproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- UniqueDiffWithinAt.monoproof · cited by 8
- tangentConeAt_closureproof · cited by 4
- Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetricproof · cited by 1
- posTangentConeAt_monoproof · cited by 0