Theorems · Theorem · convex and discrete geometry
Convex.ordConnected
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {s : Set 𝕜},
Convex 𝕜 s → s.OrdConnectedAlias of the forward direction of convex_iff_ordConnected.
- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 64 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.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Convexstatement · cited by 551
- Set.OrdConnectedstatement · cited by 161
- convex_iff_ordConnectedproof · cited by 3
Cited by19
Results whose statement or proof uses this declaration.
- ConvexOn.slope_le_of_hasDerivWithinAt_Iioproof · cited by 5
- ConvexOn.le_slope_of_hasDerivWithinAt_Ioiproof · cited by 5
- MonotoneOn.convexOn_of_derivproof · cited by 4
- StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioiproof · cited by 4
- StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iioproof · cited by 4
- StrictMonoOn.strictConvexOn_of_derivproof · cited by 4
- Convex.mul_sub_le_image_sub_of_le_derivproof · cited by 3
- Convex.mul_sub_lt_image_sub_of_lt_derivproof · cited by 3
- StrictConvexOn.lt_slope_of_hasDerivWithinAtproof · cited by 2
- StrictConvexOn.slope_lt_of_hasDerivWithinAtproof · cited by 2
- ConvexOn.slope_le_of_hasDerivWithinAtproof · cited by 1
- ConvexOn.le_slope_of_hasDerivWithinAtproof · cited by 1