Theorems · Theorem · convex and discrete geometry
Sbtw.mem_image_Ioo
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] {x y z : P}, Sbtw R x y z → y ∈ ⇑(AffineMap.lineMap x z) '' Set.Ioo 0 1- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · 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
- Set.imagestatement · cited by 5,609
- Set.Iccproof · cited by 1,702
- AddTorsorstatement and proof · cited by 1,657
- Set.Ioostatement and proof · cited by 1,214
- AffineMapstatement · cited by 674
- AffineMap.lineMapstatement and proof · cited by 254
Cited by3
Results whose statement or proof uses this declaration.
- sbtw_iff_mem_image_Ioo_and_neproof · cited by 2
- EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zeroproof · cited by 1
- sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pairproof · cited by 0