Theorems · Theorem · convex and discrete geometry
segment_eq_Icc
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {x y : 𝕜},
x ≤ y → segment 𝕜 x y = Set.Icc x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.Iccstatement · cited by 1,702
- LE.le.antisymmproof · cited by 507
- segmentstatement · cited by 120
- segment_subset_Iccproof · cited by 4
- Icc_subset_segmentproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Manifold.riemannianEDist_le_pathELengthproof · cited by 4
- ConvexOn.strictMonoOnproof · cited by 3
- segment_eq_Icc'proof · cited by 2
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- Circle.range_pathproof · cited by 2
- Convex.mem_Iccproof · cited by 2
- ConvexOn.le_max_of_mem_Iccproof · cited by 1
- Circle.path_injective_of_neproof · cited by 1
- Real.closedBall_eq_segmentproof · cited by 0