left_mem_affineSpan_pair
∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] (p₁ p₂ : P), p₁ ∈ line[k, p₁, p₂]The first of two points lies in their affine span.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Ringstatement and proof · cited by 7,463
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement · cited by 871
- affineSpanstatement · cited by 417
- Set.mem_insertproof · cited by 109
- mem_affineSpanproof · cited by 34
Cited by15
Results whose statement or proof uses this declaration.
- AffineMap.lineMap_mem_affineSpan_pairproof · cited by 5
- vadd_left_mem_affineSpan_pairproof · cited by 4
- affineCombination_mem_affineSpan_pairproof · cited by 2
- EuclideanGeometry.angle_eq_angle_div_two_of_oangle_eq_of_sSameSideproof · cited by 2
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- affineSpan_pair_le_of_right_memproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sqproof · cited by 1
- AffineMap.lineMap_rev_mem_affineSpan_pairproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_twoproof · cited by 1
- affineSpan_pair_eq_of_right_mem_of_neproof · cited by 0