Theorems · Theorem · ring theory
neg_one_sq
∀ {R : Type u} [inst : Monoid R] [inst_1 : HasDistribNeg R], (-1) ^ 2 = 1- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- MonoidHasDistribNeg
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.
- Monoidstatement and proof · cited by 3,887
- one_powproof · cited by 521
- HasDistribNegstatement and proof · cited by 114
- neg_sqproof · cited by 31
Cited by14
Results whose statement or proof uses this declaration.
- groupCohomology.comp_d₁₂_eqproof · cited by 10
- ZMod.χ₄_eq_neg_one_powproof · cited by 5
- Complex.I_pow_fourproof · cited by 4
- Matrix.det_eq_prod_roots_charpoly_of_splitsproof · cited by 3
- hasSum_one_div_nat_pow_mul_cosproof · cited by 2
- hasSum_one_div_nat_pow_mul_sinproof · cited by 2
- DirichletCharacter.even_or_oddproof · cited by 2
- neg_one_pow_twoproof · cited by 1
- qrSign.sq_eq_oneproof · cited by 1
- Nat.pow_pow_add_primeFactors_one_ltproof · cited by 1
- ArithmeticFunction.moebius_sq_eq_one_of_squarefreeproof · cited by 1
- Nat.pepin_primalityproof · cited by 1