Theorems · Theorem · order theory
mul_self_inj_of_nonneg
∀ {α : Type u_4} [inst : CommRing α] [NoZeroDivisors α] [inst_2 : PartialOrder α] [IsStrictOrderedRing α] {a b : α},
0 ≤ a → 0 ≤ b → (a * a = b * b ↔ a = b)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_antisymmproof · cited by 2,068
- NoZeroDivisorsstatement and proof · cited by 545
- neg_nonnegproof · cited by 60
Cited by9
Results whose statement or proof uses this declaration.
- Real.sqrt_eq_rpowproof · cited by 25
- Real.sqrt_mul_selfproof · cited by 14
- EuclideanGeometry.dist_smul_vadd_eq_distproof · cited by 4
- Affine.Triangle.dist_orthocenter_reflection_circumcenterproof · cited by 3
- real_inner_add_sub_eq_zero_iffproof · cited by 2
- RCLike.norm_I_of_ne_zeroproof · cited by 2
- EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eqproof · cited by 2
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1
- norm_sub_eq_norm_addproof · cited by 0