Theorems · Theorem · ring theory
Commute.neg_left
∀ {R : Type u} [inst : Mul R] [inst_1 : HasDistribNeg R] {a b : R}, Commute a b → Commute (-a) b- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- MulHasDistribNeg
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.
- Commutestatement · cited by 639
- HasDistribNegstatement and proof · cited by 114
- SemiconjBy.neg_leftproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.mul_comp_neg_Xproof · cited by 1
- IsNilpotent.exp_neg_mul_exp_selfproof · cited by 1
- NormedSpace.exp_mem_unitary_of_mem_skewAdjointproof · cited by 1