midpoint_vsub_left
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : Invertible 2] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] (p₁ p₂ : P), midpoint R p₁ p₂ -ᵥ p₁ = ⅟2 • (p₂ -ᵥ p₁)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 46 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.
- 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
- VSub.vsubstatement · cited by 817
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement and proof · cited by 268
- midpointstatement · cited by 123
- AffineMap.lineMap_vsub_leftproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- midpoint_vsub_rightproof · cited by 3
- EuclideanGeometry.mul_dist_eq_abs_sub_sq_distproof · cited by 3
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- AffineSubspace.mem_perpBisector_iff_inner_eqproof · cited by 0
- midpoint_sub_leftproof · cited by 0