Theorems · Definition · ring theory
AddOpposite.unop
{α : Type u_1} → αᵃᵒᵖ → αThe element of α represented by x : αᵃᵒᵖ.
- Defined in
- Mathlib.Algebra.Opposites
- Cited by
- 125 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddOppositestatement · cited by 452
- PreOpposite.unop'proof · cited by 0
Cited by140
Results whose statement or proof uses this declaration.
- AddSubgroup.opproof · cited by 57
- AddSubmonoid.opproof · cited by 28
- AddSubsemigroup.opproof · cited by 28
- AddOpposite.opEquivproof · cited by 20
- HahnSeries.addOppositeEquivproof · cited by 10
- AddOpposite.unop_injectivestatement · cited by 8
- AddOpposite.unop_surjectivestatement · cited by 6
- AddEquiv.opproof · cited by 4
- AddOpposite.opHomeomorph_symm_applystatement · cited by 4
- AddUnits.opEquivproof · cited by 4
- isAddLeftRegular_opproof · cited by 4
- AddSubgroup.mem_opstatement · cited by 3