Theorems · Definition · ring theory
AddOpposite.op
{α : Type u_1} → α → αᵃᵒᵖThe element of αᵃᵒᵖ that represents x : α.
- Defined in
- Mathlib.Algebra.Opposites
- Cited by
- 192 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.
- AddOppositestatement · cited by 452
Cited by214
Results whose statement or proof uses this declaration.
- AddSubgroup.unopproof · cited by 30
- AddSubsemigroup.unopproof · cited by 25
- AddSubmonoid.unopproof · cited by 25
- AddOpposite.opEquivproof · cited by 20
- AddOpposite.op_surjectivestatement · cited by 12
- Finset.addETransformLeftproof · cited by 10
- Finset.addETransformRightproof · cited by 10
- HahnSeries.addOppositeEquivproof · cited by 10
- AddUnits.embedProductproof · cited by 9
- AddOpposite.op_injectivestatement · cited by 9
- dist_add_rightproof · cited by 7
- IsCentralVAdd.op_vadd_eq_vaddstatement · cited by 6
Showing the 200 most cited of 214.