Theorems · Theorem · convex and discrete geometry
segment_subset_Icc
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : PartialOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [PosSMulMono 𝕜 E] {x y : E},
x ≤ y → segment 𝕜 x y ⊆ Set.Icc x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, 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 · 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
- PartialOrderstatement and proof · cited by 6,410
- le_reflproof · cited by 2,061
- Set.Iccstatement · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- add_le_addproof · cited by 666
- PosSMulMonostatement and proof · cited by 188
- segmentstatement and proof · cited by 120
- smul_le_smul_of_nonneg_leftproof · cited by 47
Cited by4
Results whose statement or proof uses this declaration.
- segment_eq_Iccproof · cited by 9
- segment_subset_uIccproof · cited by 2
- Nonneg.segment_eq_Iccproof · cited by 2
- Set.OrdConnected.convex_of_chainproof · cited by 1