Theorems · Theorem · ring theory
sq_eq_sq_iff_eq_or_eq_neg
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- CommRingNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Commute.allproof · cited by 119
- Commute.sq_eq_sq_iff_eq_or_eq_negproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- eq_or_eq_neg_of_sq_eq_sqproof · cited by 4
- quadraticChar_card_sqrtsproof · cited by 1
- ModularGroup.stabilizer_of_neproof · cited by 0