Theorems · Theorem · convex and discrete geometry
Wbtw.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}, Wbtw R x y z → Wbtw R z y xAlias of the forward direction of wbtw_comm.
- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 51 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
- Wbtwstatement · cited by 165
- wbtw_commproof · cited by 11
Cited by13
Results whose statement or proof uses this declaration.
- Collinear.two_zsmul_oangle_eq_leftproof · cited by 3
- EuclideanGeometry.Sphere.IsExtTangentAt.symmproof · cited by 2
- Wbtw.angle₂₃₁_eq_zero_of_neproof · cited by 2
- Wbtw.angle₁₃₂_eq_zero_of_neproof · cited by 1
- Wbtw.oangle₂₃₁_eq_zeroproof · cited by 1
- Wbtw.oangle_sign_eq_of_ne_rightproof · cited by 1
- Wbtw.oangle₁₃₂_eq_zeroproof · cited by 1
- Wbtw.left_mem_affineSpan_of_right_neproof · cited by 0
- Wbtw.left_mem_image_Ici_of_right_neproof · cited by 0
- Wbtw.wOppSide₃₁proof · cited by 0
- Wbtw.wSameSide₁₂proof · cited by 0
- Wbtw.wSameSide₂₁proof · cited by 0