midpoint_comm
∀ {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] (x y : P), midpoint R x y = midpoint R y x- Cited by
- 14 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, 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.
- DFunLike.coeproof · cited by 62,936
- 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
- Invertiblestatement and proof · cited by 549
- Invertible.invOfproof · cited by 268
- AffineMap.lineMapproof · cited by 254
- midpointstatement and proof · cited by 123
- AffineMap.lineMap_apply_one_subproof · cited by 8
- one_sub_invOf_twoproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- right_vsub_midpointproof · cited by 5
- dist_midpoint_rightproof · cited by 3
- midpoint_vsub_rightproof · cited by 3
- midpoint_vsubproof · cited by 2
- EuclideanGeometry.oangle_midpoint_rev_leftproof · cited by 2
- EuclideanGeometry.Sphere.IsDiameter.symmproof · cited by 2
- Equiv.pointReflection_midpoint_rightproof · cited by 1
- midpoint_add_subproof · cited by 1
- AffineEquiv.pointReflection_midpoint_rightproof · cited by 1
- midpoint_eq_right_iffproof · cited by 1
- EuclideanGeometry.oangle_midpoint_rev_rightproof · cited by 0
- EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eqproof · cited by 0