Theorems · Theorem · commutative algebra
CharZero.eq_neg_self_iff
∀ {R : Type u_2} [inst : NonAssocRing R] [NoZeroDivisors R] [CharZero R] {a : R}, a = -a ↔ a = 0- Defined in
- Mathlib.Algebra.Ring.CharZero
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
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.
- CharZerostatement and proof · cited by 932
- NoZeroDivisorsstatement and proof · cited by 545
- NonAssocRingstatement and proof · cited by 483
- eq_neg_iff_add_eq_zeroproof · cited by 32
- add_self_eq_zeroproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- legendreSym.eq_zero_mod_of_eq_neg_oneproof · cited by 1
- PeriodPair.derivWeierstrassP_zeroproof · cited by 1
- rotation_ne_conjLIEproof · cited by 0
- PeriodPair.G_eq_zero_of_oddproof · cited by 0
- jacobiSym.eq_neg_one_at_prime_divisor_of_eq_neg_oneproof · cited by 0
- HurwitzZeta.expZeta_zeroproof · cited by 0