Theorems · Theorem · convex and discrete geometry
openSegment_subset_segment
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : SMul 𝕜 E] (x y : E), openSegment 𝕜 x y ⊆ segment 𝕜 x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
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 · 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
- LT.lt.leproof · cited by 2,189
- segmentstatement and proof · cited by 120
- openSegmentstatement and proof · cited by 102
Cited by8
Results whose statement or proof uses this declaration.
- Convex.openSegment_subsetproof · cited by 3
- sub_mem_posTangentConeAt_of_segment_subsetproof · cited by 2
- midpoint_mem_segmentproof · cited by 1
- mem_extremePoints_iff_forall_segmentproof · cited by 1
- mem_segment_sub_addproof · cited by 1
- StarConvex.openSegment_subsetproof · cited by 0
- mem_segment_add_subproof · cited by 0
- mem_tangentConeAt_of_segment_subsetproof · cited by 0