Theorems · Theorem · convex and discrete geometry
Sbtw.ne_left
∀ {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 ≠ x- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 8 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- AddTorsorstatement and proof · cited by 1,657
- Sbtwstatement and proof · cited by 122
Cited by8
Results whose statement or proof uses this declaration.
- Sbtw.oangle_eq_rightproof · cited by 6
- Sbtw.oangle_eq_leftproof · cited by 5
- Wbtw.trans_sbtw_leftproof · cited by 2
- EuclideanGeometry.angle_add_angle_eq_of_sbtwproof · cited by 1
- Sbtw.angle₂₁₃_eq_zeroproof · cited by 0
- Sbtw.angle₃₁₂_eq_zeroproof · cited by 0
- not_sbtw_self_leftproof · cited by 0
- Sbtw.trans_right_leftproof · cited by 0