Theorems · Theorem · order theory
abs_mul_abs_self
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] (a : α), |a| * |a| = a * a- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- RingLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- absstatement · cited by 1,814
- neg_mul_negproof · cited by 32
- abs_by_casesproof · cited by 3
Cited by21
Results whose statement or proof uses this declaration.
- sq_absproof · cited by 49
- Complex.abs_re_le_normproof · cited by 9
- RCLike.abs_re_le_normproof · cited by 6
- Complex.canonicalFactor_ne_zeroproof · cited by 6
- EuclideanGeometry.dist_inversion_centerproof · cited by 5
- RCLike.abs_im_le_normproof · cited by 4
- Real.sqrt_mul_self_eq_absproof · cited by 4
- abs_le_iff_mul_self_leproof · cited by 3
- abs_mul_selfproof · cited by 2
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1
- InnerProductGeometry.angle_smul_smulproof · cited by 1