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Theorems · Definition · group theory

Units.opEquiv

{M : Type u_2} → [inst : Monoid M] → Mᵐᵒᵖˣ ≃* Mˣᵐᵒᵖ

The units of the opposites are equivalent to the opposites of the 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
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsUnit.op · cited by 3IsUnit.opAddAut.mulRight · cited by 2AddAut.mulRightIsUnit.unop · cited by 2IsUnit.unopUnits.coe_unop_opEquiv · cited by 0Units.coe_unop_opEquivUnits.coe_opEquiv_symm · cited by 0Units.coe_opEquiv_symmMonoid · cited by 3887MonoidUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valMulEquiv · cited by 1142MulEquivMulOpposite · cited by 1135MulOppositeMulOpposite.op · cited by 520MulOpposite.opMulOpposite.unop · cited by 268MulOpposite.unopMulOpposite.rec' · cited by 5MulOpposite.rec'Units.opEquivCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.