Theorems · Theorem · ring theory
eq_or_eq_neg_of_sq_eq_sq
∀ {R : Type u} [inst : CommRing R] [NoZeroDivisors R] (a b : R), a ^ 2 = b ^ 2 → a = b ∨ a = -b- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- CommRingNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- NoZeroDivisorsstatement and proof · cited by 545
- sq_eq_sq_iff_eq_or_eq_negproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.IsUnitTrinomial.irreducible_of_coprimeproof · cited by 2
- PythagoreanTriple.coprime_classificationproof · cited by 1
- Complex.real_algHom_eq_id_or_conjproof · cited by 1
- PythagoreanTriple.classificationproof · cited by 0