vsub_midpoint
∀ {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 : P), p -ᵥ midpoint R p₁ p₂ = ⅟2 • (p -ᵥ p₁) + ⅟2 • (p -ᵥ p₂)- Cited by
- 4 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.
Cites12
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 and proof · cited by 817
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement and proof · cited by 268
- smul_negproof · cited by 181
- midpointstatement and proof · cited by 123
- neg_vsub_eq_vsub_revproof · cited by 87
- neg_addproof · cited by 69
- midpoint_vsubproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpointproof · cited by 1
- AffineSubspace.mem_perpBisector_iff_inner_eq_innerproof · cited by 1
- Affine.Triangle.eulerPoint_eq_midpointproof · cited by 0
- AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zeroproof · cited by 0