Theorems · Theorem · convex and discrete geometry
mem_segment_iff_wbtw
∀ {R : Type u_1} {V : Type u_2} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [IsOrderedRing R] {x y z : V}, y ∈ segment R x z ↔ Wbtw R x y z- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, 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 and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- Wbtwstatement · cited by 165
- segmentstatement and proof · cited by 120
- affineSegment_eq_segmentproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- eq_lineMap_of_dist_eq_mul_of_dist_eq_mulproof · cited by 1
- Wbtw.sameRay_vsubproof · cited by 1
- Wbtw.mem_segmentproof · cited by 1
- dist_add_dist_of_mem_segmentproof · cited by 0