Theorems · Theorem · group theory
sub_neg_eq_add
∀ {α : Type u_1} [inst : SubtractionMonoid α] (a b : α), a - -b = a + b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 264 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 52 definitions · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- SubtractionMonoidstatement and proof · cited by 208
Cited by264
Results whose statement or proof uses this declaration.
- sub_sub_sub_cancel_rightproof · cited by 34
- sub_sub_sub_cancel_leftproof · cited by 23
- Complex.sin_sq_add_cos_sqproof · cited by 11
- RCLike.mul_conjproof · cited by 10
- MeasureTheory.SignedMeasure.toSignedMeasure_toJordanDecompositionproof · cited by 10
- Polynomial.splits_iff_exists_multisetproof · cited by 9
- Real.sinh_arsinhproof · cited by 8
- UniformContinuous.addproof · cited by 7
- max_zero_sub_max_neg_zero_eq_selfproof · cited by 6
- CauSeq.lim_negproof · cited by 6
- hasFDerivAt_ringInverseproof · cited by 5
- Matrix.det_one_add_mul_commproof · cited by 5
Showing the 200 most cited of 264.