Theorems · Theorem · convex and discrete geometry
Convex.inter
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : SMul 𝕜 E] {s t : Set E}, Convex 𝕜 s → Convex 𝕜 t → Convex 𝕜 (s ∩ t)- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Convexstatement and proof · cited by 551
- StarConvex.interproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- convex_Iccproof · cited by 29
- convex_Icoproof · cited by 9
- convex_Iocproof · cited by 8
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- Metric.exists_forall_closedEBall_subset_aux₂proof · cited by 3
- Continuous.exists_contMDiff_approx_and_eqOnproof · cited by 2
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2
- ContDiffWithinAt.exists_lipschitzOnWithproof · cited by 2
- convex_Iooproof · cited by 2
- HasFDerivWithinAt.curveIntegral_segment_source'proof · cited by 2
- Convex.quasiconvexOn_of_convex_leproof · cited by 1