Theorems · Theorem · convex and discrete geometry
segment_subset_uIcc
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : LinearOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [PosSMulMono 𝕜 E] (x y : E),
segment 𝕜 x y ⊆ Set.uIcc x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccproof · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.uIccstatement · cited by 393
- le_totalproof · cited by 294
- PosSMulMonostatement and proof · cited by 188
- segmentstatement and proof · cited by 120
Cited by2
Results whose statement or proof uses this declaration.
- Convex.combo_le_maxproof · cited by 3
- Convex.min_le_comboproof · cited by 1