Theorems · Definition · group theory
AddEquiv.opOp
(M : Type u_3) → [inst : Add M] → M ≃+ Mᵃᵒᵖᵃᵒᵖ
An additive monoid is isomorphic to the opposite of its opposite.
- Defined in
- Mathlib.Algebra.Group.Equiv.Opposite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- AddEquivstatement · cited by 1,087
- AddOppositestatement and proof · cited by 452
- Equiv.transproof · cited by 337
- AddOpposite.opEquivproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- AddEquiv.opOp_applystatement and proof · cited by 0
- AddEquiv.opOp_symm_applystatement and proof · cited by 0
- AddRightCancelMonoid.addGroupOfFiniteproof · cited by 0