Theorems · Definition · group theory
AddUnits.opEquiv
{M : Type u_2} → [inst : AddMonoid M] → AddUnits Mᵃᵒᵖ ≃+ (AddUnits M)ᵃᵒᵖThe additive units of the additive opposites are equivalent to the additive opposites of the additive units.
- Defined in
- Mathlib.Algebra.Group.Units.Opposite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- AddEquivstatement · cited by 1,087
- AddOppositestatement and proof · cited by 452
- AddUnitsstatement and proof · cited by 325
- AddUnits.valproof · cited by 248
- AddOpposite.opproof · cited by 192
- AddOpposite.unopproof · cited by 125
- AddOpposite.rec'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- IsAddUnit.opproof · cited by 2
- IsAddUnit.unopproof · cited by 2
- AddUnits.coe_opEquiv_symmstatement · cited by 0
- AddUnits.coe_unop_opEquivstatement · cited by 0