left_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), p₁ -ᵥ midpoint R p₁ p₂ = ⅟2 • (p₁ -ᵥ p₂)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 47 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.left_vsub_lineMapproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- right_vsub_midpointproof · cited by 5
- EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eqproof · cited by 1
- EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpointproof · cited by 1
- EuclideanGeometry.angle_midpoint_eq_piproof · cited by 1
- left_sub_midpointproof · cited by 0
- EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisectorproof · cited by 0