Theorems · Theorem · convex and discrete geometry
Sbtw.wbtw
∀ {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 → Wbtw R x y z- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 37 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.
Cites7
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
- Wbtwstatement · cited by 165
- Sbtwstatement and proof · cited by 122
Cited by37
Results whose statement or proof uses this declaration.
- Sbtw.left_ne_rightproof · cited by 7
- Sbtw.oangle_eq_rightproof · cited by 6
- Sbtw.oangle_eq_leftproof · cited by 5
- EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_piproof · cited by 3
- Sbtw.sOppSide_of_notMem_of_memproof · cited by 3
- Wbtw.trans_sbtw_leftproof · cited by 2
- Sbtw.oangle_sign_eqproof · cited by 2
- sbtw_iff_left_ne_and_right_mem_image_Ioiproof · cited by 2
- Sbtw.oangle_sign_eq_leftproof · cited by 1
- Sbtw.oangle_sign_eq_rightproof · cited by 1
- EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_piproof · cited by 1
- Sbtw.right_mem_affineSpanproof · cited by 1