Theorems · Theorem · convex and discrete geometry
left_mem_segment
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[ZeroLEOneClass 𝕜] [inst_4 : MulActionWithZero 𝕜 E] (x y : E), x ∈ segment 𝕜 x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- add_zeroproof · cited by 2,707
- le_reflproof · cited by 2,061
- one_smulproof · cited by 1,374
- zero_smulproof · cited by 716
- zero_le_oneproof · cited by 316
- ZeroLEOneClassstatement and proof · cited by 304
- segmentstatement · cited by 120
- MulActionWithZerostatement and proof · cited by 79
Cited by8
Results whose statement or proof uses this declaration.
- right_mem_segmentproof · cited by 7
- segment_sameproof · cited by 4
- convexHull_pairproof · cited by 3
- subset_convexJoin_leftproof · cited by 2
- Convex.isLittleO_pow_succproof · cited by 1
- Sion.exists_lt_iInf_of_lt_iInf_of_supproof · cited by 1
- convexJoin_assoc_auxproof · cited by 1
- Real.dimH_segmentproof · cited by 0