midpoint_eq_iff
∀ {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 z : P},
midpoint R x y = z ↔ (AffineEquiv.pointReflection R z) x = y- Cited by
- 7 results in Mathlib
- Foundations
- Depth 48 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.coestatement · 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
- AffineEquivstatement · cited by 191
- midpointstatement · cited by 123
- AffineEquiv.pointReflectionstatement · cited by 32
- AffineEquiv.pointReflection_midpoint_leftproof · cited by 5
- AffineEquiv.injective_pointReflection_left_of_moduleproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- midpoint_eq_smul_addproof · cited by 6
- midpoint_pointReflection_rightproof · cited by 3
- midpoint_eq_left_iffproof · cited by 2
- midpoint_eq_midpoint_iff_vsub_eq_vsubproof · cited by 1
- midpoint_pointReflection_leftproof · cited by 1
- midpoint_eq_iff'proof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_distproof · cited by 1