Theorems · Theorem · ring theory
sq_eq_one_iff
∀ {R : Type u} [inst : Ring R] {a : R} [NoZeroDivisors R], a ^ 2 = 1 ↔ a = 1 ∨ a = -1- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- RingNoZeroDivisors
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.
- Ringstatement and proof · cited by 7,463
- NoZeroDivisorsstatement and proof · cited by 545
- one_powproof · cited by 521
- Commute.one_rightproof · cited by 22
- Commute.sq_eq_sq_iff_eq_or_eq_negproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.eq_neg_one_of_two_rightproof · cited by 5
- quadraticChar_dichotomyproof · cited by 3
- DirichletCharacter.even_or_oddproof · cited by 2
- OrthonormalBasis.det_to_matrix_orthonormalBasis_realproof · cited by 2
- Complex.norm_sub_one_sq_eq_of_norm_eq_oneproof · cited by 2
- inv_eq_self₀proof · cited by 1
- Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_detproof · cited by 1
- Pell.Solution₁.eq_one_or_neg_one_iff_y_eq_zeroproof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- Algebra.discr_eq_discrproof · cited by 1
- MulChar.isQuadratic_iff_sq_eq_oneproof · cited by 1
- Int.sq_eq_one_of_sq_lt_fourproof · cited by 1