Theorems · Theorem · convex and discrete geometry
Sbtw.symm
∀ {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] [IsOrderedRing R] {x y z : P}, Sbtw R x y z → Sbtw R z y xAlias of the forward direction of sbtw_comm.
- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsOrderedRingstatement and proof · cited by 777
- Sbtwstatement · cited by 122
- sbtw_commproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_pointReflection_rightproof · cited by 3
- Affine.Triangle.oangle_excenter_singleton_eq_add_piproof · cited by 1
- EuclideanGeometry.oangle_midpoint_leftproof · cited by 1
- EuclideanGeometry.oangle_midpoint_rightproof · cited by 1
- EuclideanGeometry.angle_add_angle_eq_of_sbtwproof · cited by 1
- Affine.Triangle.oangle_excenter_singleton_eqproof · cited by 1
- Sbtw.oangle_sign_eq_of_sbtwproof · cited by 0
- Sbtw.oangle_sign_eq_of_sbtw_leftproof · cited by 0
- AffineSubspace.SOppSide.oangle_sign_eq_negproof · cited by 0
- Sbtw.left_mem_affineSpanproof · cited by 0
- Sbtw.left_mem_image_Ioiproof · cited by 0