Theorems · Definition · ring theory
MulOpposite.op
{α : Type u_1} → α → αᵐᵒᵖThe element of MulOpposite α that represents x : α.
- Defined in
- Mathlib.Algebra.Opposites
- Cited by
- 520 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOppositestatement · cited by 1,135
Cited by571
Results whose statement or proof uses this declaration.
- MulOpposite.op_injectivestatement · cited by 37
- Subgroup.unopproof · cited by 30
- Submonoid.unopproof · cited by 26
- Subsemigroup.unopproof · cited by 25
- MulOpposite.opEquivproof · cited by 24
- Matrix.mulVec_singlestatement · cited by 23
- IsCentralScalar.op_smul_eq_smulstatement · cited by 22
- MulOpposite.op_surjectivestatement · cited by 21
- MeasureTheory.Integrable.mul_constproof · cited by 17
- Units.embedProductproof · cited by 12
- Matrix.mulVec_eq_sumstatement · cited by 12
- Submodule.mulRightMapproof · cited by 12
Showing the 200 most cited of 571.