Theorems · Theorem · commutative algebra
add_self_eq_zero
∀ {R : Type u_2} [inst : NonAssocSemiring R] [NoZeroDivisors R] [CharZero R] {a : R}, a + a = 0 ↔ a = 0- Defined in
- Mathlib.Algebra.Ring.CharZero
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
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.
- CharZerostatement and proof · cited by 932
- NonAssocSemiringstatement and proof · cited by 805
- NoZeroDivisorsstatement and proof · cited by 545
- two_mulproof · cited by 232
Cited by7
Results whose statement or proof uses this declaration.
- Complex.conj_eq_iff_improof · cited by 9
- CharZero.eq_neg_self_iffproof · cited by 6
- Polynomial.X_pow_sub_X_sub_one_irreducible_auxproof · cited by 1
- LinearMap.BilinForm.toQuadraticMap_isOrthoproof · cited by 0
- CharZero.neg_eq_self_iffproof · cited by 0
- AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zeroproof · cited by 0
- LinearMap.isAlt_iff_eq_neg_flipproof · cited by 0