Theorems · Theorem · convex and discrete geometry
Wbtw.collinear
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] {x y z : P}, Wbtw R x y z → Collinear R {x, y, z}- Defined in
- Mathlib.Analysis.Convex.Between
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- AddTorsorstatement and proof · cited by 1,657
- Wbtwstatement and proof · cited by 165
- Collinearstatement and proof · cited by 79
- Set.insert_commproof · cited by 16
- collinear_insert_of_mem_affineSpan_pairproof · cited by 5
- Wbtw.mem_affineSpanproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eqproof · cited by 5
- EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_piproof · cited by 3
- Sbtw.oangle_sign_eqproof · cited by 2
- Wbtw.oangle_sign_eq_of_ne_leftproof · cited by 2
- EuclideanGeometry.cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_piproof · cited by 0
- AffineIndependent.not_wbtw_of_injectiveproof · cited by 0